Is repairing an external transmission cooler supposed to make a car stop over-heating?

An external transmission cooler is normally added in line with a vehicles already existing transmission cooler built into the radiator its function is to cool the transmission only. Adding, replacing and or repairing a transmission cooler would only benefit the transmission by cooling the transmission fluid. The transmission cooler is used mainly for cooling transmissions that pull heavy loads like trailers but is also used a lot in racing to keep the fluid cooler which helps reduce transmission overheat or burnout. , EzForJesus