The ATF from the Trans. to the Radiator comes directly from the Torque Converter, which is the hottest ATF. The purpose of the ORIFICE going into the Radiator is to restrict the flow so that the TC maintains it full and the pump maintains pressure. In the bottom of the Rad is a two pass loop, Passenger side is IN, drivers side is out, drivers side outlet can be routed to an AUX cooler mounted in front of the Radiator or straight back to the Trans.
The main purpose of the Radiator coil is for COOLING, NOT to heat the ATF. The most efficient cooling is liquid to liquid, an AUX cooler is air to liquid.
The E4OD ATF temperature will rise in a very short time, IIRC the temp needs to be only 80*F to shift from 3rd into OD.
To those that think two AUX coolers in series are more efficient, it is not so, one larger AUX cooler is much better, you don't want to present restrictions in the flow, the return ATF is used mainly to cool the trans. bearings.
An E4OD is engineered to normanly run at 180* to a 190*F, Heavy towing requires an AUX cooler sized to fit the load requirements.