Why did the Roman soldiers tear down Herod's temple stone by stone?

Les teaches that Matthew 24 opens with Jesus leaving the temple, and when His disciples pointed out the temple buildings, He predicted that not one stone would be left upon another. He was looking ahead to the Roman siege under Titus, which devastated the city. Les notes that Josephus, though not Scripture, records that the Roman soldiers had heard a rumor that immense gold and other wealth was hidden between Herod's temple's building stones. Soldiers being soldiers, they tore it down stone by stone looking for that supposed hidden wealth. Whatever the reason, Les says, that is what happened: the temple was utterly destroyed, not by fire as Nebuchadnezzar destroyed Solomon's temple (which was mainly cedar from Lebanon and burned), because Herod's temple was predominantly stone with precious gold and silver. It was exactly as Jesus said—thrown down stone by stone, leaving only the little segment of the western wall now known as the Wailing Wall.