[Bigdav160]

Heat is bad for the transmission fluid. It loses it's lubrication properties near 300 degrees. In a modern overdrive transmission this could happen in the torque converter if it remains unlocked for too long under load.

Today they engineer the trans fluid to go to the radiator cooler first. It helps bring the engine coolant up to temp more quickly for emission compliance. The in radiator "liquid to liquid" is highly efficient. If an external "air to liquid" cooler is installed it's after the radiator so the trans fluid can be cooled even further.