Source: H. Graetz, History of the Jews, volume II (Philadelphia: Jewish Publication Society of America, 1893) 307.
"For a whole night and the next day the fire raged fiercely; then Titus commanded that it should be extinguished, and that a road should be leveled for the advance of his legions. A council of war was hastily summoned to decide upon the fate of the Sanctuary. This council consisted of six of the chief generals of the army, three of whom advised the destruction of the Temple, which, if spared, would inevitably remain as a focus for rebellion. Titus was opposed to this decision, partly on account of the Princess Berenice's feelings, and three of the council agreeing with their leader, it was decided to take the Temple, but not to destroy it."
This overlaps with what I wrote in Josephus and Titus: Spin, Spin, Spin and Unremarkable Agrippa. In the first post, I quoted an article that maintained that Josephus tries to present Titus favorably, in contrast to certain Roman sources, which depict him as a monster. In the second one, I cited sources that said Berenice's husband, Agrippa II, was both pro-Roman and pro-Judaism.
Graetz seems to follow Josephus' positive portrait of Titus. And how do we know that's wrong? Maybe Titus acted out of character, since he was friendly with elements of the Judean political establishment.
Can people ever act out of character? Many New Testament scholars have contended that the Gospels' portrayal of Pontius Pilate is inaccurate, since they say Pilate wanted to let Jesus go, whereas historical sources depict him as a blood-thirsty tyrant. But why couldn't Pilate have acted out of character every once in a while?