I recently just bought 2 RROD Xbox 360's off Ebay after doing a bit of research on common Xbox 360 RROD problems. I must admit, I quite enjoy getting my hands dirty with this sort of thing and being a long time PC builder, this exercise was quite easy.
Upon initial inspection of the console, the previous owner had attempted an xclamp fix and had got thermal paste absolutely everywhere. It took a while to clean all this off and re-apply some Artic Silver.
After turning the console for the first time I got the error code 0031 which appears to be a Southbridge Issue. Undeterred by this, I tried pushing down on the Southbridge chip and then powering up again - which unbelievably actually worked, green lights to be had all round! I applied some pressure on the chip with a clamp and then gave the Hot air gun a spin for a while. Now the Xbox 360 boots without issue and works for long periods without a single fail.
Sometimes you get lucky, some fixes take no time at all.
The last thing I need to do is fix the fan as it sounds like an Aircraft carrier at full throttle:
Xbox 360 fixed RROD loud fans
If you are going to try and do this yourself, be aware that there are quite a few bricked 360's for sale which are usually due to a failed attempted at patching a 360's DVD firmware.
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List of Xbox 360 RROD error codes and how to determine what error you have can be found HERE>