Although I agree overheating is probably the cause, I thought I'd share a story with you in case it applies to your problem.
My computer, when new, used a PII 266. After a year and a half I thought I'd upgrade it. To upgrade I used one of the so called "slotket" cards. (Slot 1 to PPGA Socket 370 converter) This allowed me to use a PPGA Celeron in my system, so I bought a 400 PPGA and installed it with no problems. About 3 months later I started getting strange reboots and lockups after about an hour of playing any game. Eventually I discovered hard drive errors and replaced my harddrive. The problems started again soon after. Finally I found the problem, my slocket card was losing contact in the processor slot when the system warmed up and the metal heatsink expanded! If you use one of these slocket cards I recommend you check to make sure it fits securely in the processor slot after your system has warmed up. (The standard PII retention clips don't work on my slocket, but I found cable ties make a perfect substitute.)
I thought I'd mention this because I know many people use slocket cards to run Celerons in PII slots. (They work great for this. Many of the new slockets even have jumpers for setting core voltage and FSB speed built right onto them.

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bloom25
THUNDERBIRDS