In fact, if you really want to do your tranny a favor, get a standalone cooler, mount it under the front of the car with it's OWN cooling lines coming straight from the tranny, and put a small electric fan on the cooler, and that tranny will run very cool all the time. Why run hot fluid through a HOT radiator? That doesn't cool anything...a radiator is meant to cool WATER and nothing else!
I tried this in my car but ended up going back through the radiator trans cooler. I had a big cooler, but no fan. Temp were going over 200 regularly in traffic. Back through the radiator cooler and temps are back in line around 170