I've seen a few viruses do similar things before, but there are several things it could be. The first thing I would do is boot into safe mode, just spam the F8 key while it's booting up and eventually you'll get a menu giving you some boot options, just hit safe mode. Play around for a bit and see if it reboots.
If it doesn't, it's a software issue, I would go to http://free.antivirus.com/hijackthis/ and post your hijackthis log here, or PM me or something (idk if there is a PM system on here to be honest)
If it still reboots then it is probably hardware, but there is still a possibility of a boot sector virus executing shutdown -t shellcode with a random number of minutes.
If it's a hardware issue there are a lot of possible culprits, if you have a rail going out on the power supply, you could be getting intermittent power. There are a lot of things it could be but those are the most likely.
Oh and if it's getting hot, overheating is an issue. If it was an apple I'd say the firmware on the fan was corrupted.