I had a dell when I was in school that developed a heat related problem. It was summer and when the room temperature got to about 80 it would crash. Then it would work ok when the room cooled down.
I had a 3 year extended warranty. First Dell sent someone to change the fan unit. Then they sent someone to change the mother board. Then there were a couple more organ transplants--it can't remember what. Then when it got to the point they were going to send someone to change the video card, and by then I had spent a week of my life talking to one technician after another, finally a guy who was up there on the dell support food chain decided this was nuts. He called my computer in for an autopsy. They gave me a (sorta) new one (refirbished). It worked out for me cause the one the gave me had a faster chip and more memory.
What I learned out of this is that the same thing happens to computers when they overheat as happens to e34 engines. Progressive part failures.
I hope your experience does not turn out to be as frustrating as mine was. Good luck.
Dinan chip, Bilstein sports w H&R, RD sways, RD strut brace, 750 bushings, Zimmermans/MetalMasters, O.E. M Pars, Eisenmann muffler