Most things that transmit power has losses (pumping losses, frictional losses, etc)
and those losses are normally in the form of heat
If there were no losses, there would be no heat generated and *ALL* the power would
be transmitted. In this case the driven axles
The harder it has to work, the more heat is generated
That is 'part' of the metrics used by the design team(s) to derive the 'ratings'
Getting close to those ratings will have it heat up and close to or at the rated
thermal range of the component. In this case the differenttial
Going above it's ratings will have it heat up more and more until the lube failes
Even catching fire
Age of the fluid lube also part of the equation and if it is beyond it's life
span (spec), it will NOT lube it well enough and reduce the axle rating
Why the OPs got hot can be either, or both, or some other factor we do not know
For it to radiate enough heat to actually 'feel' the differece is up there and
wonder what condition the OPs diff is in.
Suggest as a min, change/flush the diff fluid and recharge with OEM recommended
fluid lube...or better
The OP's sig says the TV is a 3/4 ton HD, so upped in ratings from a regular 3/4 ton
and say that because higher class than a half ton can also be over it's ratings...
Tuner?
Over sized tires?
Spirited right foot...like mine?