Modern Motherboards with inbuilt video and most modern video cards, as well as most modern monitors can be set up to switch off (by Windows - and presumably other OSes as well - some MB bioses have the power saving built in) after a certain period of time for power saving - this should also reduce the heat.

Since someone allegedly switched the PC on, I'd say that either someone accessed the internet from the PC, then to cover their tracks, or just to set a fire for the purpose of covering their tracks, if not just deliberate malicious arson.

Robin