If routine maintenance isn't performed over the lifetime of a computer, heat can cause damage to the motherboard and capacitors. Check the inside of the tower and look for leaking or bulging capacitors. If you see such, then you'll need a new motherboard. In addition, make sure to blow out all the dust by used compressed or canned air, specially around the heatsink, processor, and all fans and vents. And then, if you have the experience, it would be a good idea to replace the heatsink thermal paste with a new, thin layer.. If the paste is old and cracked, it won't dissipate heat quickly and could easily cause the thermal shutdown you've been seeing.
Hope this helps.
Grif
My computer is an old HP desktop with windows 7. It was working great until this christmas when i went to visit some family for the whole month and left the pc off. When i got back it worked for a few weeks and then it shot down. Then the fans would start spinning for a second and then turn off, then spin for a second and turn off again. This will go on endlesly. I got a new psu and it "fixed" the problem for a few days. Then it started doing the same thing.

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