Huh, this should be interesting.
BMW is amazingly silent on "all things towing".
-They do not 'rate' their vehicles as tow vehicles; no GCWR, no GVWR.
-The hitch has a rating, but is installed by dealers- not the company that makes the vehicle. This absolves them of such requirements.
- Unlike most cars and trucks, there is no altered maintenance or transmission maintenance for heavy towing applications
I suspect that they decided that their 'exposure' to warranty issues is very limited since 95-98% of owners will never tow, and those that do will tow rarely. Any issues due to transmission overheating, etc, will be limited and just cheaper to deal with the handful that occur within the warranty period than deal with the confusion and expense of 'severe duty maintenance'.
But I'm a cynic. Others will surely say "those BMW engineers thought of it and no coolers and no altered maintenance is the very best plan to get 200-300k out of your X5 as a tow vehicle".
So....
Unfortunately we have no clue as to how hot the FRIGGING ENGINE gets in our X5d, let alone tranny!!!! BMW engineers have determined that us americans would be confused by an engine temp gauge, so thats gone... dropping in a SPA gauge with tranny and engine temp would be sweet, especially if you will be towing a lot. EGT would be good too. (Have all 3 on my tow vehicle, F250 PSD)
But to answer your question (

) : No, no cooler "required"
A