I bought a used PS3 that arrived DOA with this problem. I did a lot of research on how to fix it, but my technical skills aren't that great so there wasn't anything I wanted to try. Then I swear to god I ran across a fix that so far has worked for me and you don't even have to disassemble the machine. Put the
PS3 in its box (or another) with the rear vents facing out. You can also just wrap it in a towel. I wound up doing both as all I had was a larger box. Use a hair dryer running it back and forth across the length of the vents for 5 minutes. Let it rest for a minute, do another 5 minutes, let it rest a minute, then do a final 5 minutes and set the unit someplace relatively cool and let it cool down for about an hour.
I plugged it in and it worked. There are several videos on YouTube that use this method. That's where I originally saw this fix.
Will it last? Don't know, but so far I have had no problems.