I've been running my tranny lines through a cooler only. I use normal size hard lines and then convert to a hose at the cooler. No radiator.
I drive fairly easy for the first few miles or so to warm it up before I jump on it. Been that way for about a dozen years.
I have a supercharger on a stroked small block and I did not want to add any heat from the tranny to the radiator since the motor runs a little warm.
Beware if you are in a cold climate like the other member posted.