The CPU is just one part. Other parts can become heat sensitive.
Since you did try the old cover off trick, what are you doing to replace, upgrade components to fix it? I start by adding 100 or more Watts to the power supply. Where do you start?
When I use the computer for a while it shuts down completely without any warning. To start it again I have to shut of the power switch for a short while.
The problem seems to be temerature related since it works better if I open it and lead some cool air from outside into it. But if the problem is that the cpu is overheated, why do I have to shut of the power? It doesnt make any sense to me?