If the PS has had issues for a while, the battery may be dead too. That can sometimes cause weird problems.

Can you short the "clear BIOS" jumper and/or replace the button battery? The battery is often a 2032 (20 mm diameter, ~ 3.2V).

(If it had to do with the heat sink, I would think that you would have some time before the CPU got too hot and shut down, so I don't think that's the main problem.)

HTH a little. Good luck!

Cheers,
Scott.