Sounds like a processor overheating to me - mine did that when the fan clip broke, on my P4. If you enter BIOS, there should be a menu like PC health status that can tell you how hot the processor is, and how hot it is before it turns off. If the temp. gets high, check your fan is in one piece and functioning correctly.
In Windows, I use a program called SpeedFan to check the temp. of my PC.