I just had one on my bench recently. It appeared to be overheating, but wasn't. It turned out to be the 0ohm resistors on the lines that relay temperature info. Three out of the six were measuring well over an ohm. They are supposed to read 0.3ohm no higher. In this units case it was old bad solder, fresh solder restored all 6 to 0.3ohms and the false overheat went away.
This is a different board. Someone damaged it and tore the pads and traces, ignore that, this is just for illustration purposes. The area circled in red, the yellow lines are where the 0ohm resistors should be. Test those resistors. They should be 0.3ohm, a small margin of error is okay (like say 0.4). If they measure close to or higher than 1 ohm either the solder has gone bad or the resistor has gone bad.
They are very small, the testing isn't hard but the work is a pinch difficult/delicate. Anyway overheat issues on 360 s aren't always apu, as I was trying to state before. If you search "xbox 360 S false overheat" you may even find videos of people showing this repair.
[image|3304426]