Being a data loving techno-geek, I stuck a temperature sensor in there. Modern differentials use hypoid gears, which have a "sliding" interaction, which shears the oil and generates heat.

Normal driving, minimal load: Rarely more than 50 degrees over ambient.

Towing: Usually 50 to 100 degrees over ambient

Grinding up long grades (20+ minutes) with heavy loads: I've seen 150 over ambient. 255 on a 105 degree day.... That's pretty stinkin' hot, and I don't recommend the touch test!

This is with Mag-Hytek cover and Redline 75W140 synthetic.