Computer shutting down during gaming.

I noticed that the CPU runs at 40 degrees celcius on idle. That was a couple of weeks ago.

last night my pc shuts down more frequently that usual. even on idle. about every 30 minutes. I opened the case. Fan is working.
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Then this morning my pc shut down. Turns on for a second and shuts down again.

Turned off the pc (and unplugged it, ofcourse), CPU heatsink is hot. very hot.

Thermal paste is dried out.

Suggestions?

Get a new fan? Or simply reapply thermal paste?

The CPU doesnt look damaged. No smells. No burn marks. Just the Thermal paste that looks dried out.

Got it! Thanks