It definitely is important. I started a thread a while back about using engine coolant to heat the transmission. Mine was thinking about manual transmissions, but automatics are even more temperature sensitive. Most automatic transmission coolers are also warmers where the engine coolant helps heat the oil, but once it is up to temperature, it also cools it down.
Anyway, here is a link to my thread. There are several links to studies done on the effect of transmission oil temperature that you can check out.
https://ecomodder.com/forum/showthre...ant-29872.html