Warning message Apple TV overheating

Did you try using some can'ed air to blow the dust out from the inside yet?

Also make sure you give it some breathing room, you don't want to cook in a closed cabinet with other hot gear.

It is most likely the on board temp sensor. The only thing I can think of would be to disassemble everything right down to the board and do a solder re flow, by either using a heat gun to bring the board up to temperature so all the solder points re connect or you can also do this in an oven. This method is for repairing cold solder joints on the board, which could be the cause if the machine heated up enough to melt the solder and cause it to loose its contact. Try Google and search for "Solder Reflow"