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The problem with EOC in automatics is not overheating but lack of lubrication. The pump is only running when the engine is running, and if the pump is not running there are moving parts inside the transmission that are not getting fresh lubricant.
As for the benefits of an external cooler, as was stated your radiator also serves as a transmission cooler. This is probably more than adequate unless you do a lot of towing or frequently drive up steep hills. A trans temp gauge would help you determine if the fluid is ever getting very hot.
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