I checked for the cpu fan etc. when I first got this problem few months back. Everything is OK. I do not even screw the cpu box cover panel now. It can be slide open any time so that to cool the inner if required. I do not have air conditioning or so in my computer room, and our environment are a bit on hotter side. This also affects the machine.
I noticed that if I run old programs which do not use process much, there is no shut down, no matter how long I use it. For example I can use Adobe Flash Player 9 without any problem, but 10 or above shuts the machine after few minutes.
Last time it got shut down on antivirus scan for whole hdd. Though old version of same antivirus ran OK.
As it is difficult to get old versions now and also since I use this machine just for processing type background jobs, I found that suspending the new programs when it crosses 70% or more, helps. I can do it, say pause the anti virus when it goes on high cpu use, but it requires me to sit before it.
If Process Tamer does it, I can have this old machine still of use.