They can burn because they weren't entirely of stone. Stone has immense compression strength- it is hard to squeeze a rock to make it smaller- and it is very heavy. These qualities make it very useful for a wall. But those qualities and its tendency to crack under tension make it very difficult to use for things like rafters, joists, floorboards- so the Temple of Claudius likely had stone walls and perhaps columns but any upper floors and the roof system would have been of wood. Whether it was repairable once it burned is another question- a hot fire can damage a stone wall, and once the wood framing on the interior of the temple was burnt, the walls might well have been weakened on the interior side and collapsed inwards. And if there was rebellion in the countryside - in the case of Boudicca- people might have had better things to do than painstakingly rebuild it.