CPU problem

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Hi, i have a problem with a computer and i think the problem is the cpu, the pc was used as a testing server before and now i am using it but frequently it get blocked or restart alone, i thought about a cpu problem and discovered that more than 70% of che cpu coolear was blocked by dust and i took it away by hand,the computer now goes better but continues to get blocked sometimes,now what i want to know is if the problem is that i haven't pulished the cooler the right way or i have to change the coolear because maybe the dust inside it creates problems or the thermal paste has problems.
Thank you.