I've had this problem on 2 PC's and it was bl88dy nightmare, so much so that I gave up entirely on the first one. All I can tell you is that its probably a hardware rather a software problem. On my current PC I finally solved it myself (after having engineers out twice) by replacing the SATA cable (Hard drive to motherboard), but as Kerplunk said it could be overheating, and not necessarily the processor, could be a graphics card (if you have one) or even a card not seated properly and expanding as the PC heats up.
Have a look at your system event log (Click Start>run>type eventvwr>click ok and look for any warnings and error messages. You may get a clue about what component is causing the problem.
If Kerplunk's suggestion identifies the problem as overheating, obviously replacing broken fans or adding another will help. You could try disconnecting and reseating cards and memory chips and cables. Use an antistatic wrist strap (Maplin �1,99) if you do that and don't wear polyester!
Let us know how you get on.