|Could be overheating. That's the most common cause of random shut downs.|
If your PC boots up a little while after, it's most likely shut off because your CPU/GPU got too hot.
If it does boot up again, I'd suggest downloading CoreTemp, a piece of software that lets you view the temperatures.
Usually takes a few minutes or so before you can boot the PC again after an overheat.
PEBMAC - The biggest cause of Computing problems.
Damn ID10T Errors.