Can you recommend any methods to help me fix my xbox's RROD problem?

Hello, recently my xbox has fallen ill to the RROD. I am not sure of the exact reasons, but I’m guessing leaving the xbox on the carpet (after moving to a new house and being careless in its location) wasn’t a good idea. Nor leaving the power pack there either.

My xbox isn’t under warranty, and I don’t really want to send it into a shop to get fixed when I can probably just sell it for parts and buy a new one for cheaper.

What I would like to know is if anyone has fixed their xbox from this problem themselves, and what methods they used. I would prefer it if it was something a complete beginner (ie me) could do, and if it was a cheap solution.

Thanks for the help.