If it's old, out of warranty, and there's no chance of a repair or replacement from whoever you bought it from, then why not crack it open and take a look inside? If the only issue is that fan is broken and its overheating causing the freezes, then I'm sure you can fix it yourself. Chances are you can get a replacement fan somewhere, and even if it's not an 'official' one you can probably replace it with a PC cooling fan instead. Better to try that than just give up and lose your money.
As an aside though, I would never buy a second-hand console even if I were desperate. It's one of those products that just isn't worth it because you can never tell how much it has been used and abused. The same goes for racing wheels and various other things.