I built my PC about 2yrs ago and have not had any issues. I only use it for gaming mainly and have played hrs of games, but I started playing Skyrim recently and my system just crashed on me. I updated my drivers, did a virus scan and cleaned the registy and it is still happening. I cleaned out the case and the cpu fan looks good. I did finally see the CPU temp error, so I checked the BIOS (before it shut down again) and the cpu temp got to 85c. I did not apply thermal paste when I installed the CPU, which is an I7-950, since I thought the heatsink fan already had it. When I cleaned the cpu fan, there appeared to be very little paste on the cpu, so I have ordered some, but I wondered if there could be other issues I need to check or if this is most likely the issue. I built my PC with the following:
gtx570 overclocked gpu
asus p6x58d premium m/b
corsair 750w psu
windows 7 64bit premium
In all probability, if the CPU overheating caused the system to shutdown, there is very little chance of it being seriously damaged, but the possibility is still there. It might be worth using a test like prime95 to test the cpu, if it can withstand it for 30 mins to an hour I'd say it was fine.
Skyrim is a pretty resource intense game, but your system shouldn't have any problems with it. If it was running smoothly up until this, the only problem i can see would be the CPU overheat.
If you don't have one already, a good CPU cooler is not a bad way to blow $30-50. I had this one and it's not bad: