CPU Overheating

[ddmx]

Is it a possibility?

Conditions:
If pc has been off for a while then it will start up, shuts down some 5-20 minutes later.
If pc has just locked up or shut down automatically, won't start up right away. If I wait a while I can repeat at step 1.
Shuts down in cpu intensive tasks as well as just browsing the net.

What I've tested:
Replaced gpu to no avail.
Replaced mobo to no avail.
Replaced HD to no avail.
Tested ram to no avail.
Booted up outside of case with only mobo, 1 stick ram, cpu and gpu, it did boot ruling out bad components...

In the bios I booted it up for the last time and noticed a cpu temp of 85C. Obviously, this is not good. The fan over the cpu however was still running (heatsink?). Is there a chance that I need to reapply thermal paste and possibly get a new heatsink?

I have a bad habit of leaving the comp run 24hrs a day for a few days in a row and did this all throughout the summer noticing my room temperature at least 10 degrees hotter than the rest of the house.

Thoughts? Any input is much appreciated!

[Shadow]

In the bios I booted it up for the last time and noticed a cpu temp of 85C. Obviously, this is not good.

That kinda narrows it down.

Remove the fan, check the cpu for anything unusual, if it looks fine remove the old thermal paste from both fan and cpu, apply new paste and see if it fixes the problem.

[ShackAttack12]

Yep, reseat that heatsink. Also make sure dust hasn't built up in the fins of the heatsink and in the fan.