Rear differential

Not too hot to put your hands on the housing after a long drive. If you ever have the displeasure of burning one up from trying to get unstuck in snow or mud, you will run for your life from the smell when the cover is removed. Skunk spray smells like perfume compared to burned-up gear lube!

As for the actual temperature, I do not know of anyone who has ever measured it. Noise is the first symptom when there is a problem.