It’s called the three way valve. It’s primarily used to bring the ATF up to temperature, not So much to cool it. The max temp my atf has ever been is 209. Not hot. That’s flogging the truck up the big I15 hills towards St George in 100 degree heat pulling 8600 pounds of boat. Anyways, failure of the three way valve is Definitely heard of, if not common. I would not at all call it part of the transmission though. So his transmission didn’t fail but an outside part may have which could cause the trans to fail.
Yeah he said his trans was at 260 degrees or something crazy. I’ve seen mine at just north of 200 when towing my camp trailer up big hills.