Xbox shutting down due to overheating without being hot

That's not too hot at all for the console. If it were, the console would shut down due to overheating.

That looks good. The Xbox may feel hot around the vents, but that is normal as the heat is being ventilated. You should be maintaing normal function, unless the console shuta down from overheating that will indicate an issue. If you are not experiencing
shut downs, it is most likely normal heat as the Xbox processes the games.

Define "very hot". The exhaust temperature on an original 360 is around 95F. On a 360 S, it's 135F.



Is it an original 360, or the new 360 S design?



If it's an original, are both fans spinning in the back? If it's a 360 S, is the fan spinning?



Does the console shut down due to overheating?

It shuts down due to overheating and displays the overheat warning upon restart.

Sounds like an ongoing issue for the developer to fix as it's being happening for a while now according to the posts on the forum's. Maybe the game is just too big for the xbox to handle without it overheating and shutting down.