I agree, mostly likely overheating. Check the fans. If you know how to check the Event Logs (under control panel >> administrative tools) you may see a message about why it shut down (giving a hint if it's memory, hard disk, graphics card).
This happens a lot with laptops, but also can happen with towers. My desktop started doing that, and it turned out to be my graphics card overheating - I got a new one and it was fine.
There is a freeware utility that you can install that will tell you the internal termperatures - can't remember what it's called, but search through the tech support board for overheating and maybe someone's posted it.