It's a very common problem this and can be caused by loads of different things. It's odd though that recently I've had the same symptoms caused by the same disease.
Basically a PC slowing down and eventually locking up or crashing, looking at the BIOS the CPU temperature is very high!
If you then look at the CPU fan and heatsink it's like the inside of vacuum cleaner. Remove all the dust put the Heatsink back on and off we go. PC runs stable.
My son's PC had this with his graphics card, games crashing and locking up. The heatsink / fan on the graphics card, same treatment though worked like a charm.