There's a TEMPORARY way to fix the Xbox. It works, but i wouldn't recommend it as a permanent solution. I don't know what manner of fire hazard it presents, but mine didn't combust or anything. Better yet, MS still replaced it, so it doesn't void the warranty, either.
1) Unhook everything from your Xbox apart from the power cable. This includes faceplate and HDD.
2) Wrap it in a bunch of towels, block the ventilation holes.
3) Turn it on
4) Leave it on for half an hour.
5)Unwrap it, turn it off.
5) Leave it to cool for 30 minutes to an hour. A windowsill is a good idea.
6) Hook everything back up. Turn it on.
It works for roughly FIVE DAYS (it did for me). In that time, it rarely crashes except for when your time's nearly up. I expect you can do this indefinitely, except that it would eventually degrade and destroy.
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I got that one from CheapAssGamer.