Using a computer that reboots at random makes for a tense life.
I've just resolved a problem where a computer would restart for no good reason - often when busy, suggesting a thermal connection, by swapping the RAM.
Before this, I'd tried everything else including a clean install.
RAM is very cheap these days, I paid AU$70 for two 1GB SO-DIMMS.
I'm on an Intel Mac Mini at the moment and it was rebooting at least once a day, usually during intense CPU activity, such as playing video. After a reboot, I'd go looking in /Library/Logs for a panic.log file and it wasn't there. That should have been the clue.
Anyway, with new RAM it's now been running for about two weeks with no problems.
If you experience random reboots, try swapping the RAM.