I cannot believe that a simple right angle drive box should be more than very slightly above ambient temperature even after "active" use.

If it is too hot to touch then there is massive friction, caused either by incorrect assembly, incorrect machining or no lubricant, or all three!

I'll check the temperature of the differential on my car tomorrow, and report. Bet it is barely warm to the touch.

Peter,
66, 2016 Porsche Boxster S
No longer driving Tarka, the 2014 Plus 8...