So, I'm attempting to fix my buddy's 360... he's got one of the consoles from release, so, I'm suprised it lasted this long!
When I got his 360, it would boot, and play for ~5 min. before shutting down, and throwing the overheating error. The outside was pretty dusty, so I could only imagine what the inside was like. Once I got it open, I used some compressed air and dusted everything off nicely, took the heatsinks off, shined them up all nice and pretty and applied some AS5. Booted up the system, and it still would only play for about 5 minutes before throwing a 0013. So, I figured I'd try the x-clamp mod on it. Booted the system up, and to my suprise, I played Halo 3 for about an hour, before I decided to shut it off, and test again in the morn. Morning comes... 0013 again. Instantly this time. So I messed around with the tightness of the heatsinks, and at one point got the system to run for about 3 hours before it threw 0013 again.
I honestly don't know what else to try, so if anyone has any ideas on how to get rid of this, what seems like, rare error code, I'd love you forever.

Thanks in advance!
0013 is ram overheating so it is a cooling issue you should try to install heatsinks on them(thermalpads on the bottom ram, then the case absorbs the heat)...
Doing the 12V-fanmod might fix it as well...
It is a cooling issue so try to keep the system as cool as possible...