1 horsepower of heat is ~~ 12,000 BTU per hour so one needs to know how much slippage loss in horsepower is being lost.
A liquid to air heat exchanger depends on the delta between the two temperatures but usually drops the input to out temperature by 10-15-20F only.
Think about the 150,000 BTU engine radiator vs a 15,000 BTU transmission radiator.
10 quarts of ATF weighs about 17 pounds so 17 BTU might cool it 1F in 1 hour so 17 x 60 = 1020 btu might cool it 1F in 1 minute so 10200 BTU might cool it 10F in 1 minute.
The flow rate is 2.5 quarts per minute.
The question is not how fast you cool at STEADY state ATF but how fast it get reHEATED back in transmission.
Around 15,000 btu seem ideal except for really hot places where the ambient exceeds 100F.
Under WOT a quarter mile will probably create 5% slip or 15 HP of heat for 15 seconds 180,000 btu/4= 45,000 btu how many minutes do you want to wait until it cools down ................15,000 = 3 minutes
The 176F normal ATF would increase by 45F to 221F in the quarter mile run.
The above uses water and we all know ATF is much less efficient [50%] at heating up and cooling than water so at worst it might be double.
The problem is if the ATF id half as efficient as water then the heat stays in the metal so the TC and clutches might go up 90F while ATF goes up 45F and the metal would take longer to cool.
Engine coolant [50/50] is 50% more efficient than ATF.
http://www.engineeringtoolbox.....html
The following patent has equations which will help you calculate an exact load:
http://www.patentstorm.us/pate....html
Confused? I am a little since they just GIVE a thermal mass of 23 BTU/F for a combination of ATF, aluminum and steel disregarding heat flowing back into engine block and radiated into the air/body from transmission case.