I don't have the T56 but do have some experience with coolers. My 2010 Roush has the 5r55 auto, I do track days with that and started having trans overheating issues almost immediately and that point my trans will then start shifting itself into overdrive, even though turned off.
I added a Mishimoto Auto Trans cooler with a fan and had it mounted in front of my radiator to the top right hand side of the radiator. I also added a switch inside the car to be able to turn the fan on and off as well a Boss 302 gauge pod with a trans temp Gauge. Turns out the fan on that trans cooler was causing negative back pressure on my radiator and actually causing my engine temp to get hotter. Pulled that one and installed a B&M Racing 20,500 BTU cooler without a fan in the same location. It helps keep the temp down longer, but it will still start to overheat my trans after about 3 sessions on track.
I have also added a Kenny Brown/Fluidyne Triple Flow Triple Pass radiator and the same heat exchanger with dual fans. Also Roush 7 bar front grille and MMD hood vents to get additional air flowing under the hood.
My trans temp has been up to 250*, at roughly 220* it starts shifting into overdrive. Ran at Road America 4th of July weekend and I was between 210 and 230 by the end of every session, but surprisingly this year it never shifted into overdrive, even though outside temps were also very hot. My supercharger also has a lot to do with all the extra heat they create, but I have never really had any problem with the engine overheating, just the trans. I also recommend you take axis101 advise above and call Kenny Brown and see if they can provide some more info on cooling the T56. Not the same situation but hope this helps a little.
I've now run almost 60,000 miles and 30 track days and my trans has not failed yet!!! Knock on wood....