Titus gives orders not the burn the Temple.

Titus proposed to these that they should give him their advice what should be done about the holy house. Now some of these thought it would be the best way to act according to the rules of war, [and demolish it,] because the Jews would never leave off rebelling while that house was standing; at which house it was that they used to get all together. Others of them were of opinion, that in case the Jews would leave it, and none of them would lay their arms up in it, he might save it; but that in case they got upon it, and fought any more, he might burn it; because it must then be looked upon not as a holy house, but as a citadel; and that the impiety of burning it would then belong to those that forced this to be done, and not to them.

But Titus said, that "although the Jews should get upon that holy house, and fight us thence, yet ought we not to revenge ourselves on things that are inanimate, instead of the men themselves;" and that he was not in any case for burning down so vast a work as that was, because this would be a mischief to the Romans themselves, as it would be an ornament to their government while it continued. So Fronto, and Alexander, and Cerealis grew bold upon that declaration, and agreed to the opinion of Titus. Then was this assembly dissolved, when Titus had given orders to the commanders that the rest of their forces should lie still; but that they should make use of such as were most courageous in this attack. So he commanded that the chosen men that were taken out of the cohorts should make their way through the ruins, and quench the fire.

4. Now it is true that on this day the Jews were so weary, and under such consternation, that they refrained from any attacks. But on the next day they gathered their whole force together, and ran upon those that guarded the outward court of the temple very boldly, through the east gate, and this about the second hour of the day. These guards received that their attack with great bravery, and by covering themselves with their shields before, as if it were with a wall, they drew their squadron close together; yet was it evident that they could not abide there very long, but would be overborne by the multitude of those that sallied out upon them, and by the heat of their passion. However, Caesar seeing, from the tower of Antonia, that this squadron was likely to give way, he sent some chosen horsemen to support them. Hereupon the Jews found themselves not able to sustain their onset, and upon the slaughter of those in the forefront, many of the rest were put to flight. But as the Romans were going off, the Jews turned upon them, and fought them; and as those Romans came back upon them, they retreated again, until about the fifth hour of the day they were overborne, and shut themselves up in the inner [court of the] temple.

So Titus retired into the tower of Antonia, and resolved to storm the temple the next day, early in the morning, with his whole army, and to encamp round about the holy house. (But as for that house, God had, for certain, long ago doomed it to the fire); and now that fatal day was come, according to the revolution of ages; long ago doomed it to the fire; and now that fatal day was come, according to the revolution of ages; it was the tenth day of the month Lous, [Ab,] upon which it was formerly burnt by the king of Babylon; although these flames took their rise from the Jews themselves, and were occasioned by them; for upon Titus's retiring, the seditious lay still for a little while, and then attacked the Romans again, when those that guarded the holy house fought with those that quenched the fire that was burning the inner [court of the] temple; but these Romans put the Jews to flight, and proceeded as far as the holy house itself.

At which time one of the soldiers, without staying for any orders, and without any concern or dread upon him at so great an undertaking, and being hurried on by a certain divine fury, snatched somewhat out of the materials that were on fire, and being lifted up by another soldier, he set fire to a golden window, through which there was a passage to the rooms that were round about the holy house, on the north side of it. As the flames went upward, the Jews made a great clamor, such as so mighty an affliction required, and ran together to prevent it; and now they spared not their lives any longer, nor suffered any thing to restrain their force, since that holy house was perishing, for whose sake it was that they kept such a guard about it.

6. And now a certain person came running to Titus, and told him of this fire, as he was resting himself in his tent after the last battle; whereupon he rose up in great haste, and, as he was, ran to the holy house, in order to have a stop put to the fire; after him followed all his commanders, and after them followed the several legions, in great astonishment; so there was a great clamor and tumult raised, as was natural upon the disorderly motion of so great an army.

Then did Caesar, both by calling to the soldiers that were fighting, with a loud voice, and by giving a signal to them with his right hand, order them to quench the fire. But they did not hear what he said, though he spake so loud, having their ears already dimmed by a greater noise another way; nor did they attend to the signal he made with his hand neither, as still some of them were distracted with fighting, and others with passion.

But as for the legions that came running thither, neither any persuasions nor any threatenings could restrain their violence, but each one's own passion was his commander at this time; and as they were crowding into the temple together, many of them were trampled on by one another, while a great number fell among the ruins of the cloisters, which were still hot and smoking, and were destroyed in the same miserable way with those whom they had conquered; and when they were come near the holy house, they made as if they did not so much as hear Caesar's orders to the contrary; but they encouraged those that were before them to set it on fire.

As for the seditious, they were in too great distress already to afford their assistance [towards quenching the fire]; they were every where slain, and every where beaten; and as for a great part of the people, they were weak and without arms, and had their throats cut wherever they were caught. Now round about the altar lay dead bodies heaped one upon another, as at the steps going up to it ran a great quantity of their blood, whither also the dead bodies that were slain above [on the altar] fell down.

7. And now, since Caesar was no way (able to restrain the enthusiastic fury of the soldiers, and the fire) proceeded on more and more, he went into the holy place of the temple, with his commanders, and saw it, with what was in it, which he ...found to be far superior to what the relations of foreigners contained, and not inferior to what we ourselves boasted of and believed about it. But as the flame had not as yet reached to its inward parts, but was still consuming the rooms that were about the holy house, and (Titus supposing what the fact was, that the house itself might yet he saved, he came in haste and endeavored to persuade the soldiers to quench the fire), and gave order to Liberalius the centurion, and one of those spearmen that were about him, to beat the soldiers that were refractory with their staves, and to restrain them; yet were their passions too hard for the regards they had for Caesar, and the dread they had of him who forbade them, as was their hatred of the Jews, and a certain vehement inclination to fight them, too hard for them also

Moreover, the hope of plunder induced many to go on, as having this opinion, that all the places within were full of money, and as seeing that all round about it was made of gold. And besides, one of those that went into the place prevented Caesar, when he ran so hastily out to restrain the soldiers, and threw the fire upon the hinges of the gate, in the dark; whereby the flame burst out from within the holy house itself immediately, when the commanders retired, and Caesar with them, and when nobody any longer forbade those that were without to set fire to it. And thus was the holy house burnt down, without Caesar's approbation.

8. Now although any one would justly lament the destruction of such a work as this was, since it was the most admirable of all the works that we have seen or heard of, both for its curious structure and its magnitude, and also for the vast wealth bestowed upon it, as well as for the glorious reputation it had for its holiness; yet might such a one comfort himself with this thought, that it was fate that decreed it so to be, which is inevitable, both as to living creatures, and as to works and places also. However, one cannot but wonder at the accuracy of this period thereto relating; for the same month and day were now observed, as I said before, wherein the holy house was burnt formerly by the Babylonians. Now the number of years that passed from its first foundation, which was laid by king Solomon, till this its destruction, which happened in the second year of the reign of Vespasian, are collected to be one thousand one hundred and thirty, besides seven months and fifteen days; and from the second building of it, which was done by Haggai, in the second year of Cyrus the king, till its destruction under Vespasian, there were six hundred and thirty-nine years and forty-five days. (The Works of Flavius Josephus War of the Jews Book 6 Chapter 4)

Commentary

The temple was one of the seven great wonders of the ancient world! (A large part of Herod’s rebuilding of the Temple was completed before his death in 4 BC, however, many do not know that the work of rebuilding still continued for almost 68 years after his death. The work was not entirely finished until 63 AD, which was only 7 years before it’s destruction in A.D. 70!)

First the Jews themselves set fire to the court of the temple, and afterwards the Romans. Fire consumed the buildings and the temple went up.  

The  Roman soldiers were acting against the orders, of Titus and set the Temple of fire. In a wild frenzy they rushed in and set the Temple on fire.  WHY? It was not within God’s will that one stone be left upon another of the Temple that represented the old Mosaic, system. (Matthew 24:1)

This whole time God was building a temple, a spiritual tabernacle to dwell in that was not made with hands. 1 Corinthians 3:16 Do you not know that you are the temple of God and that the Spirit of God dwells in you?

The apostle James recognized God was rebuild the tabernacle of David, and that it would include Gentiles, Acts 15:13-18 (NKJV) 13 And after they had become silent, James answered, saying, “Men and brethren, listen to me:14 Simon has declared how God at the first visited the Gentiles to take out of them a people for His name. 15 And with this the words of the prophets agree, just as it is written: 16 ‘After this I will return And will rebuild the tabernacle of David, which has fallen down; I will rebuild its ruins, And I will set it up; 17 So that the rest of mankind may seek the LORD, Even all the Gentiles who are called by My name, Says the LORD who does all these things.’18 “Known to God from eternity are all His works.”

Paul tell us that Christ is the chief cornerstone of that Temple. Ephesians. 2:19-22 (NKJV) 19 “Now, therefore, you (Gentiles) are no longer strangers and foreigners, but fellow citizens with the saints and members of the household of God, 20 having been built on the foundation of the apostles and prophets, Jesus Christ Himself being the chief cornerstone, 21 in whom the whole building, being fitted together, grows into a holy temple in the Lord, 22 in whom you also are being built together for a dwelling place of God in the Spirit.”

After the destruction of the temple in 70 AD, the Sadducees disappear - no temple meant no sacrifices, no place therefore for a priestly class; total national humiliation.