You would be supprised how hot these things can get.
Its just an idea that the temp. measuring system on your mobo isnt working, or is giving an incorrent reading. It might be worth changing the bios settings to, at least, have the fan spinning.
When you say the computer turns off... does the power reset itself (and the computer trys to start again) or does the system power down?
Also, it might be worth checking if you have any thermal compound on the heatsink... if not then your temp could be 20degC higher than with it
PS. make sure it makes a decent seal with the processor.
(it also might just be worth changing the compound)
These are only heat issues with the processor... but it could be other hardware that could be causing the problem. What are your specs? But I don't see why the comp. should stop working after a time of good service