It depends on the load on the engine and the outside temperature. Heat is a transmission's worst enemy, so if you're towing trailers or moving a heavy vehicle like a motorhome or a 1-ton truck around, definitely use an auxiliary cooler. In very cold weather, the radiator-mounted "cooler" becomes a heater, warming up the fluid to at least coolant temperature and keeping condensation evaporated out. Some people add some T fittings and ball valves to isolate the cooler during below-freezing weather.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!