Since noone replied, i will. I don't think it will make a considerable difference, unless it is very large.
The tranny has a very cool property. It is a 350 lb heatsink. With the heat transfer that takes place between the water in the radiator, and the tranny fluid, if you keep the tranny down to, say 140, on a hot day, then when you hit the hill, that 350 lbs will help keep the coolant cool. You will have a longer duration on the grade, so to speak, before the fan kicks in, and before ECT begins to elevate.
Those who have complained of high trans temps, are experiencing the symptoms of hot water. Not the other way around.
Now the gotchya. A TOC that big, will overcool in the winter. So long as you have it thermostatically controlled, or even a valve to bypass, you should be golden.