I don't understand how you can conclude the trans cooling is inadequate when something else is amiss. Might save some time and expense to have transmission diagnosed at a trans shop.

I have over 118,000 Texas miles on a heavily modified 4.6. Trans has Dinan software and I change the fluid and filter about every 40,000 miles with ZF fluid. Never a problem with cooling or anything else. That is anecdotal but poor OE trans cooling hasn't been a common thread here to best of my memory. Just FYI.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas