Update: After dissembling my pc, I found that the thermal paste is applied correctly and nothing strange is going on. My computer now can function but the cpu thinks it's much hotter than it actually is. (90 or so degrees celsius)
This message was posted on behalf of Intel Corporation
In regard to your inquiry, if the PC is not throttling, getting freeze or going off by itself, then the processor should be fine, those are the first symptoms of overheating. It is expected when you play a game for the processor to reach 100% of CPU usage.
On the following link you will find a tool that does an overall test on the processor, including temperatures, so, if the processor passed the test, then it is working fine, second option to the left to install it:
Any questions, please let me know.