As others have mentioned, your auto trans probably already has a cooler built into the radiator. So, do check and verify. If so, then your car's engine temp gauge will give you the information needed to determine if you need and auxiliary cooler. An over heating trans will impart that heat into the engine's cooling system. When the heat goes beyond the capacity of the radiator, the engine temp climbs. This is your que to back off the power and reduce speed until the temp goes back to normal. It also tells you that you need an auxiliary cooler for the trans which should be placed in the feed line going to the radiator to "pre-cool" the fluid going into the radiator.
I had to install a trans cooler on my truck when I was towing a trailer. It was okay on the flats, but in the mountains, the temp gauge would only allow speeds of 35-40 going up hill, or the engine temp would go up out of sight. The trans cooler added 20-30 mph to my "climb speed" depending on altitude. Before the cooler, I did toast the trans fluid once, while I learned what the engine temp gauge was telling me. But, not since.
If you don't have a temp gauge on your engine, get one if you are going to tow trailers and/or drive in mountainous territory.
Cheers,