well, if its not in the bios or power settings, then the power supply is suspect.
And if you tested the power supply and that seems ok, and you suspect the processor cooling fan, then take the side off, put a house fan on and turn it on so it blows on the processor and the mobo and see if that stops the problem from happening. If it does then it may very well be the cooling fan.
I would also suspect the heat sink may not be seated correctly, maybe the puter was jarred at some point or something similar happened, or maybe somehow worked its may loose. So even if you go so far as to take it off and clean it up and put more thermal grease on and re-seat the hs/fan/cpu, that may do the job for you. Or if you have another hs/fan for this, you could install that one and see if it makes a difference. You didnt mention what cpu you are working with. Amd needs more cooling than most intel chips do, mhz being equal. And you didnt mention if you have any extra parts around or if you could get them, and what you experience level is.
Not a bad idea to check all connections that you can think of, power from power supply to cpu, etc, etc.
Also, if you could swap out the power supply with another power supply to test it, that would be good. Not everyone has one around or can get one easily though.