Bizarre Computer Fault that University 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?

this could be the fault of the power supply. It may be weak, so one could change that and test it again. Another thing that it could be is the memory. Ram chips can cause this, so I would run memtest first and then pull all of them, and try one stick at a time.
One more thing that it could be also, is a bad capacitor. Look at all the capacitors on the motherboard and make sure that none of them are beginning to show signs of being "blown."

Good luck, and keep us posted.