220 for modern ATF synthetics is not hot at all. Warm, but not hot.
The warning chime for my truck comes on around 265 or 270?
You can put another cooler on as you have said but there really is no reason too. The problem also it if you do cool off the tranny then those BTU's will go into the engine coolant stack and that can cause problems too.
Not saying to not put another ATF cooler in the stack, I'm just telling you some of the drawbacks because very few on this site seems to want to talk about those.
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