In brief
The transmission fluid has its own working context.
Useful to know
HELLA regards the oil cooling of the automatic transmission as a specific application of a heat exchanger. It is not the same as choosing a engine oil cooler. [1]
First specify the exact transmission, not just the make of the car. A model series can have different performances and connections. A temperature complaint must be associated with the operating mode and measurements of the system. Don't take a universal normal number from another gearbox. Here the important principle is the distinction of the serviced node and its heat regime.
Sources
For further detail and to check the information: