Gah! Pooters!

Does anyone have any idea why an otherwise perfectly healthy computer would just randomly reboot every now and again? Sometimes it goes for a couple of days without doing it. This afternoon it has done it 6 times in 15 minutes!
I’m fairly convinced it has something to do with power supply to the motherbord as I hear the fairly hefty fan on the Athlon chip cut out, I now have a UPS in case it was flaky domestic power but it is still rebooting. Any ideas on what to do now would be most appreciated