Josephus, The Jewish War Book VI Chapter IV (Cornfeld translation)
(1) The walls resistant to the battering rams
When by the eighth of the month of Lous two of the legions had completed the embankments, Titus ordered the rams to be posted opposite the western portico of the outer court of the sanctuary. The previous six days before their arrival, the most powerful of the siege engines had incessantly battered the wall without result; like the others, it made no impact on the huge and perfectly bonded stones. Another team tried to undermine the foundations of the northern gate and after great exertion succeeded in levering out the outer stones, but the gate, which was hung on the inner stones, stood firm, till, despairing of all attempts with engines and crowbars, the Romans set up ladders against the porticoes. The Jews were in no hurry to intervene, but when they climbed up, they vigorously attacked them; some were thrust back and hurled down headlong, others were encountered and slain; many, as they stepped off the ladders, were unable to shield themselves with their bucklers and were cut down with swords. Some ladders, crowded with men, were pushed sideways from above and thrown to the ground, not, however, without inflicting considerable losses. Romans who had brought up the standards fought fiercely around them, realizing that it would be a terrible disgrace if they were captured. But eventually the Jews captured even these ensigns, destroying all who had mounted the ladders. The remainder, demoralized by the fate of the fallen, withdrew. Of the Romans no one died without having achieved something. Among the rebels, all those who had distinguished themselves in previous action fought gallantly once more in this instance; among them Eleazar, nephew of the tyrant Simon. But when Titus realized that his attempts to spare a foreign temple resulted in the injury and slaughter of his troops, he ordered the gates to be set on fire.
Setting fire to the gates and porticoes
By now the troops were already setting fire to the gates; the silver melted all over quickly, admitting the flames to the solid woodwork, whence it fastened in a dense mass onto the porticoes. When the Jews saw the ring of fire, they lost all power of body and mind; because of their consternation and terror, no one attempted to extinguish the flames; thus paralyzed, they stood looking on. Yet, in their dismay at this destruction, they did not have the sense to preserve what was still left intact, but only increased their rage against the Romans, as if the whole sanctuary had already burst into flames. All through that day and the following night the fire prevailed, for the whole range of the porticoes could not be ignited at once, but only one segment after another.
(3) Titus' consultation with his staff
The next day Titus, having ordered a division of his army to put out the fire and to make a road to the gates in order to facilitate the ascent of the legions, summoned his generals...After the other prefects and tribunes gathered, Titus brought up for discussion the fate of the sanctuary. Some thought that the law of war should be enforced, since the Jews would not cease to rebel as long as the Temple remained a rallying point from every quarter. Others argued that if the Jews abandoned it, and no one placed any weapons there, it should be saved, but in case they mounted it again for military purposes, it should be burned...
Titus' declaration followed by the extinction of the flames
But Titus declared that even if the Jews were to mount it and fight from it, he would not make way on inanimate constructions instead of men nor, whatever happened, burn down such a magnificent edifice; for it would be the Romans who would lose thereby, and if it were preserved, the empire would gain a unique monument...Titus thereupon...ordered the...men...to clear a road through the ruins and put out the fire.
(4) The ninth and tenth days of Ab (Sept. AD 70)
Exhaustion and shock had depressed the energies of the Jews throughout that day; but on the next, having recovered their strength and confidence, they sallied out around the second hour through the east gate and attacked the Roman troops who occupied the outer court of the Temple. The Romans stood their ground and met the onslaught by sheltering behind a solid wall of shields held out in front of them and closed their ranks; but it was evident that they could not hold out for long against the fanatical fury of their assailants, who surpassed them in numbers. Caesar...anticipated the collapse of the line, now rushed to their assistance with picked horsemen. The Jews could not withstand their charge and, when their front ranks fell, the rest withdrew...this lasted till about the fifth hour of the day when the Jews were overpowered and shut up in the inner Temple courts.
(5) The Temple burned despite Titus' orders
Titus retired to the Antonia, intending to launch a full scale attack the following day at dawn and take possession of the Temple. The sanctuary, however, had long before been condemned by God to the flames; and now, after the passing of the years, the fated day was at hand, the tenth of the month of Lous - the very date when centuries before it had been burned by the king of Babylon. But now it was their own people who had caused and started the conflagration. For when Titus had withdrawn, the rebels shortly after attacked the Romans again, and a clash followed between the guards of the sanctuary and the troops who were putting out the fire inside the inner court; the latter routed the Jews and followed in hot pursuit right up to the Temple itself. Then one of the soldiers, without awaiting any orders and with no dread of so momentous a deed, but urged on by some supernatural force, snatched a blazing piece of wood and, climbing on another soldier's back, hurled the flaming brand through a low golden window...As the flames shot up, the Jews let out a shout of dismay that matched the tragedy; they flocked to the rescue, with no thought of sparing their lives or husbanding their strength; for the sacred structure that they had constantly guarded with such devotion was vanishing before their very eyes.
(6) The ferocity of the Roman army
A runner brought the news to Titus while he rested in his tent after the battle. Leaping up as he was, he ran to the Temple to extinguish the conflagration. He was followed by all his generals, and these, in turn, by the excited legionaries, with the shouting and confusion characteristic of a disorganized rush by such a large force. Caesar, both through voice and a raised hand, waved to the combatants to put out the fire; but his shouts were not heard, as their ears were deafened by the overwhelming din, and his beckoning hand went unheeded amid the distractions of the fight and the avenging fury. No exhortation or threat could now restrain the impetuosity of the legions; for passion was in supreme command. Crowded together around the entrances, many were trampled down by their companions; others, stumbling on the smoldering and smoke-filled ruins of the porticoes, died as miserably as the defeated. As they drew closer to the Temple, they pretended not even to hear Caeser's orders, but urged the men in front to throw in more firebrands. The rebels were powerless to help; carnage and flight spread throughout. Most of the slain were peaceful citizens, weak and unarmed, and they were butchered where they were caught. The heap of corpses mounted higher and higher about the altar; a stream of blood flowed down the Temple's steps, and the bodies of those slain at the top slipped to the bottom.
(7) Caesar's vain attempt to save the Temple
When Caesar failed to restrain the fury of his frenzied soldiers, and the fire could not be checked, he entered the building with his generals and looked at the holy place of the sanctuary and all its furnishings, which exceeded by far the accounts current in foreign lands and fully justified their splendid repute in our own. As the flames had not yet penetrated to the inner sanctum, but were consuming the chambers that surrounded the sanctuary, Titus assumed correctly that there was still time to save the structure; he ran out and by personal appeals he endeavored his men to put out the fire, instructing Liberalius, a centurion of his bodyguard of lancers, to club any of the men who disobeyed his orders. But their respect for Caesar and their fear of the centurion's staff...were overpowered by their rage, their detestation of the Jews, and an utterly uncontrolled lust for battle. Most of them were spurred on, moreover, by the expectation of loot, convinced that the interior was full of money and dazzled by observing that everything around them was made of gold. But they were forestalled by one of those who had entered into the building, and who, when Caesar dashed out to restrain the troops, pushed a firebrand, in the darkness, into the hinges of the gate. Then, when the flames suddenly shot up from the interior, Caesar and his generals withdrew, and no one was left to prevent those outside from kindling the blaze. Thus, in defiance of Caesar's wishes, the Temple was set on fire.
(8) The Temple destroyed on the anniversary of the previous conflagration
Deeply as one must mourn the destruction of the most wonderful edifice ever seen or spoken of, whether for its structure, size, and lavish perfection of detail, or the repute of its holy places, yet we may find very real comfort in the thought that fate is inexorable, not only in regard to living beings but also in regard to structures and places. We may wonder, too, at the accuracy of the cycle of fate; for it awaited, as I said, the very month and day on which the Temple had been burned by the Babylonians...
Josephus, The Jewish War Book VI Chapter V (Cornfeld translation)
(1) The scenes of horror and massacre attending the fire
While the Temple was ablaze, the attackers plundered it, and countless people who were caught by them were slaughtered. There was no pity for age and no regard was accorded rank; children and old men, laymen and priests, alike were butchered; every class was pursued and crushed in the grip of war, whether they cried out for mercy or offered resistance. Through the roar of the flames streaming far and wide, the groans of the falling victims were heard; such was the height of the hill and the magnitude of the blazing pile that the entire city seemed to be ablaze; and the noise – nothing more deafening or frightening could be imagined. There were the war cries of the Roman legions as they swept onwards en masse, the yells of the rebels encircled by fire and sword, the panic of the people who, cut off above, fled into the arms of the enemy, and their shrieks as they met their fate. The cries on the hill blended with those of the multitudes in the city below; and now many people who were exhausted and tongue-tied as a result of hunger, when they beheld the Temple on fire, found strength once more to lament and wail. Peraea and the surrounding hills, added their echoes to the deafening din. But more horrifying than the din were the sufferings. The Temple Mount, everywhere enveloped in flames, seemed to be boiling over from its base; yet the blood seemed more abundant than the flames and the numbers of slain greater than those of the slayers. The ground could not be seen anywhere between the corpses; the soldiers climbed over heaps of bodies as they chased the fugitives. The rebel horde managed with difficulty to push through the Romans, and to break through to the outer courts of the Temple Mount and from there to the city, while the surviving populace took refuge on the outer porticoes. Some of the priests at first tore out from the Temple roof the spikes with their lead sockets and hurled them at the Romans; but subsequently, as they did not achieve anything and the flames leaped towards them, they withdrew to the wall, which was eight cubits wide, and stayed there. However, two men of note, who were in a position either to save their lives by going over to the Romans or to stay there and face the same fate as the others, threw themselves into the fire and were consumed with the Temple; they were Meirus son of Belgas, and Josephus son of Dalaeus.
(2) Burning of the surrounding area and destruction of the people
The Romans, deeming it useless to spare the surrounding buildings now that the Temple was in flames, set fire to them all, both of what remained of the porticoes and all the gates, except two, one of the east gates and the southern gate, both of which were later demolished. They burned also the treasury-chambers, which contained huge sums of money, vast quantities of raiment, and other precious belongings; here, in fact, was the general depository of Jewish wealth, where the rich had brought the contents of their dismantled homes for safe keeping. They now reached the last surrounding portico of the outer court, on top of which poor women and children of the populace and a mixed multitude, numbering six thousand, had found respite/reprieve. Before Caesar could reach any decision or give any orders to his officers as regards these people, the soldiers, carried away by their fury, set fire to the porticoes from below; consequently, many were killed as they threw themselves out of the flames, while others were consumed by the blaze; of all that multitude not a soul escaped.
The people deluded by false prophets
The people owed their destruction to a false prophet who had, on that very day, declared to the people of the city that God ordered them to go up to the Temple courts to receive there the signs of their deliverance. Many prophets had been induced in these days by the rebel leaders to deceive the people by exhorting them to wait for help from God and thereby to reduce the flow of deserters, as well as buoy up with hope those who were beyond fear or precaution. Man is quickly persuaded in adversity; and when the deceiver actually holds out a prospect of release from the prevailing horrors, the sufferer falls wholly prey to these expectations.
(3) Portents and omens of the end of days
This is how the unhappy people were beguiled at this stage by charlatans and false messengers of God, while they disregarded and disbelieved the unmistakable portents that foreshadowed the coming desolation, and, as though thunderstuck [sic], blind, senseless, paid no heed to the clear warnings of God. It was like this when a star that looked like a sword stood over the city and a comet that continued for a whole year. Then again, before the war and the events that led to it, while the people were assembling for the Feast of Unleavened Bread, on the eighth of the month Xanthicus  at the ninth hour of the night so bright a light shone round the altar and Temple that it looked like broad daylight; and this lasted for half an hour. The inexperienced regarded it as a good omen, but it was immediately interpreted by the sacred scribes in conformity with subsequent events. During the same feast a cow brought by someone for sacrifice gave birth to a lamb right in the midst of the Temple courts; furthermore, the east gate of the inner sanctuary was a very massive gate made of brass and so heavy that it could scarcely be moved every evening by twenty men; it was fastened by iron-bound bars and secured by bolts that were sunk very deep into a threshold that was fashioned from a single stone block; yet this gate was seen to open on its own accord at the sixth hour of the night. The Temple guards ran and reported the news to the captain and he came up and by strenuous efforts managed to close it. To the uninitiated this also appeared to be the best of omens as they assumed that God had opened to them the gate of happiness. But wiser people realized that the security of the Temple was breaking down of its own accord and that the opening of the gate was a present to the enemy; and they interpreted this in their own minds as a portent of coming desolation.
Then again, not many days after the feast, on the twenty-first of the month of Artemisium, a supernatural apparition was seen, too amazing to be believed. What I am now to relate would, I imagine, have been dismissed as imaginary, had this not been vouched for by eyewitnesses, then followed by subsequent disasters that deserved to be thus signalized. For before sunset chariots were seen in the air over the whole country, and armed battalions speeding through the clouds and encircling the cities. Then again, at the feast called Pentecost, when the priests had entered the inner courts of the Temple by night to perform their usual ministrations, they declared that they were aware, first, of a violent commotion and din, then of a voice as of a host crying, “We are departing hence.”
Jesus’ woeful outcries four years before the war
A portent still more alarming had appeared four years before the war at a time when profound peace and prosperity still prevailed in the city. One Jesus the son of Ananias, an uncouth peasant, came to the feast at which every Jew is expected to put up a tabernacle for God; as he stood in the Temple [courts], he suddenly began to cry out: “A voice from the east, a voice from the west, a voice from the four winds, a voice against Jerusalem and the sanctuary, a voice against the bridegroom and the bride, a voice against the whole people.” Day and night he uttered this cry as he went about all the alleys. Some of the leading citizens, seriously annoyed at these ominous pronouncements, laid hold of the man and beat him savagely. But he, without uttering a word in his own defense, or for the private information of those who were beating him, persisted in uttering the same warnings as before. Thereupon, the magistrates, rightly concluding that some supernatural impulse was responsible for his behavior, took him before the Roman governor. There, although flayed to the bone with scourges, he neither begged for mercy nor shed a tear, but raising his voice to a most mournful cry, answered every stroke with “Woe, woe to Jerusalem!” When Albinus, the governor, asked him who he was and whence he came and why he uttered these cries, he made no reply whatever, but endlessly repeated his dirge over the city, until Albinus released him because he judged him insane. Throughout this time, until the war broke out, he never approached another citizen nor was he seen talking to any, but daily, like a prayer that he had memorized, he recited his lament “Woe, woe to Jerusalem!” He never cursed any of those who beat him from day to day nor did he thank those who gave him food; his only response to anyone was that melancholy prediction. His voice was heard most of all at the festivals. So, for seven years and five months he continued his wail, his voice as strong as ever and his vigor unabated, till, during the siege, after seeing the fulfillment of his foreboding, he was silenced. He was going his rounds, shouting in penetrating tones from the wall, “Woe, woe once more to the city, and the people and the Temple”; then when he added a last word, “and woe to me also!” a stone hurled from the ballista struck him, killing him on the spot. Thus, with the same forebodings still upon his lips, he met his end.
(4) The oracles
Anyone who ponders these things will find that God does care for people, and by all sorts of ways shows his people the means of salvation, while it is to folly and evils of their own choosing that they owe their destruction. Thus the Jews, after the demolition of the Antonia, reduced the Temple [area] to a tetragon, though their oracles warned them that when the Temple would become four square, the city and the Temple would fall. But what incited them more than anything else to the war was an equivocal oracle also found in their sacred scriptures, announcing that at that time a man from their country would become ruler of the world. This they took to mean someone of their own race, and many of their scholars misinterpreted it, when in fact the oracle pointed to the accession of Vespasian who was proclaimed emperor. For all that, it is impossible for people to escape their fate even if they see it coming. The Jews interpreted some of these prophecies to suit themselves and treated the others with contempt, till the fall of their country and their own destruction proved their folly.
 Nissan. Cf. John 11:55, Acts 21:26-27
 21 Iyar, Omer 36
 Precisely two weeks later
Bavli Gitin 56b
מָה עָשָׂה (טִיטוּס)? תָּפַשׂ זוֹנָה בְּיָדוֹ וְנִכְנַס לְבֵית קׇדְשֵׁי הַקֳּדָשִׁים, וְהִצִּיעַ סֵפֶר תּוֹרָה וְעָבַר עָלֶיהָ עֲבֵירָה, וְנָטַל סַיִיף וְגִידֵּר אֶת הַפָּרוֹכֶת, וְנַעֲשָׂה נֵס וְהָיָה דָּם מְבַצְבֵּץ וְיוֹצֵא, וּכְסָבוּר הָרַג אֶת עַצְמוֹ...
Avos d'Rabbi Nosson 1:6
...טיטוס הרשע...היה מורה בידו והיה מכה על גבי המזבח ואומר, "לקוס! לקוס! את מלך ואני מלך! בוא ועשי עמי מלחמה! כמה שוורים נשחטו עליך? כמה עופות נמלקו עליך? כמה יינות נסכו עליך? כמה בשמים קטרו עליך? אתה הוא שמחריב את כל העולם?!"...
אָמַר רַב יְהוּדָה אָמַר שְׁמוּאֵל וְאִיתֵּימָא רַבִּי אַמֵּי וְאָמְרִי לַהּ בְּמַתְנִיתָא תָּנָא מַעֲשֶׂה בְּאַרְבַּע מֵאוֹת יְלָדִים וִילָדוֹת שֶׁנִּשְׁבּוּ לְקָלוֹן. הִרְגִּישׁוּ בְּעַצְמָן לְמָה הֵן מִתְבַּקְּשִׁים, אָמְרוּ, "אִם אָנוּ טוֹבְעִין בַּיָּם אָנוּ בָּאִין לְחַיֵּי הָעוֹלָם הַבָּא"...כֵּיוָן שֶׁשָּׁמְעוּ יְלָדוֹת כָּךְ קָפְצוּ כּוּלָּן וְנָפְלוּ לְתוֹךְ הַיָּם...וַעֲלֵיהֶם הַכָּתוּב אוֹמֵר "כִּֽי־עָ֭לֶיךָ הֹרַ֣גְנוּ כׇל־הַיּ֑וֹם נֶ֝חְשַׁ֗בְנוּ כְּצֹ֣אן טִבְחָֽה (תהלים מד:כג)".