Bizarre Fault that Univeristy IT department cannot work out

Hey,
Here is hard one. I have a 5 year old computer (miniserver) at work, that runs on server 2003. It had been an awesome machine to use but just the other week it has been randomly rebooting. There is no blue screen that appears, the machine will suddenly just restart, sometimes several times an hour sometimes just once a day.
We have run virus scans with 3 differenet virus software packages all updated and the machine is totally clean.
Also just yesterday I left the machine in a very cold room and left the computer on all day to back up my files and it was fine, there was no rebooting at all.
I leave this machine on constantly and have never switched it off in the past 3 years. Could this problem be due to the PSU cutting out and rebooting the machine for some reason (i think because its a server the psu probably has a system in place to do that to prevent damage??)
Well thats all i can come up with has anyone got an advice or has experiences this before?

It could be a heat related issue.

The fact that you left it in a cold room without problems make it seem that's the case. Have you ever cleaned out the case with compressed air? See if the fans/intakes are clogged and go from there.