Is it a traditional torque-converter type transmission?

I'd say fhe temp increase is a combination of the engine and transmission, but I would think the biggest contributor is the engine. Under load a diesel engine heats up quickly but on overrun or low-load conditions they cool quickly too.

In winter conditions, the temp gauges in my Passat and Mondeo diesels used to drop noticeably on the long descent into Manchester from the summit of the M62, even though I was maintaining a steady 75 / 80 cruise. The gradient is such that only the faintest whiff of throttle is needed to maintain cruising speed, and the rush of very cool air was able to overcool the engine.

As mentioned the thermal efficiency of a diesel engine decreases significantly under heavy load and it would appear that you are reaching the full capacity of your cooling system. An auto box doesn't help as not only does it produce heat itself but as a result of the losses producing that it increases the demand on the engine.

Diesels do not produce much head under low load, hence some large 4x4 have aux heaters for cold weather. The internal temp gauge is unless as it intended to point to the mid-point unless the engine is very cold or a fault occurs.

The thermostat only controls the min temperature not the max. Basically is closed until running temperature is reached, then open enough to ensure the min. temperature is maintained or exceeded. It reacts relatively slowly so temperature spikes will occur.

Under low load you maybe require 25Kw of energy but under load you may well be using 75Kw of energy, that is a lot of kettles and hence the heat.

If you are worried about temperature then maybe get beefed up oil cooler fitted. These are costly until hence often manufactures do the minimum. IMHO worthwhile if you tow often and intend to keep the 4x4 for a while.