Try this, it should tell you your CPU and other temps - then post them here if you think they look a bit hot.
Does the computer turn off seemingly randomly or just after you've had it on a while? If it's just after you've had it on a while then leave it until just before it usually turns off (since it'll probably be a lot cooler once you've first booted it up.)
WOW 80c, you have a cooling problem there. My cores are always in flames because speedfan has low temps set to it. But what kind of cooling are you using?