I'll throw down a stupid question or two:
Are you sure it is full? Typically a bearing that is running in an oil bath needs to be full to 1/3 of the depth of the roller, give or take. Being empty means not enough lube = heat.
Yes, it is full.
Are you sure it isn't overfilled? Too much oil means too much resistance = heat. In this case, I think some would leak out the breather.
It is "slightly overfilled", according to the factory, by 1/2 qt. Reason: Google Dodge axle failures & you get 430,000 hits in 0.48 seconds. Before i bought my first Dodge, I researched this. I was corresponding with 24 or 26 (it's been a while) people who bought their truck brand new, had no leaks, was filled to factory levels & seviced only by dealer, who had axle failures under warranty. Every single one of the "Official final Reports" were identical---"pinion bearing failure due to lack of lubrication". Well, if it was filled to the correct factory fill level & there were no leaks, how could this happen ???
What weight oil are you running? Have you plotted viscosity curves for that oil? Many oils can survive higher temps without loss of viscosity.
Running Factory Mopar full synthetic 75 w 90. Just had to have the rear locker actuator/tone ring replaced under warranty. I think it failed due to the heat.
It has been over 15 years since I worked with gear drive designs, but we used to figure that we had issues around 150 over ambient temp. IIRC.
Are you getting abnormally low mileage? If something is overheating your oil, it has to be dragging on your system to the point of noticeable.
It is a Power Wagon so, yeah, mileage is BAD. Always has been since new. 8-10 mpg. period. Less towing.
Have you lifted the rear end and spun the wheels by hand to see if everything moves freely?
Yes, they move by hand. I check that every time I rotate or switch tires from summer to winter.
I am as stumped as you. I did buy an analog & digital food thermometer & will check with those against the IR one in the next few days or so. Lots going on right now. Pouring rain today---finally, we need it here.