The auto trans gives off more heat than you think. Anyway that's my story and I'm stiiicckken to it.
The efficiency of an automatic transmission is pretty good; somewhere in the upper 90's percentage-wise.
It's about 770 watts per horsepower if I recall. Here's chart showing how much heat is produced:
As HP passes through the trans, 1% to 5% (anyone know numbers?) of it turns to heat. 100HP engine power generates 770 watts of transmission heat.
Put a 750 watt spaceheater inside a small metal enclosed box and see how hot it gets. If there wasn't a safety switch, it would reach 500, 600, 700 degrees in minutes. The spinning torque converter dumps some heat, as does the cast body, the rest depends on that cooler.
(Even a little Rambler with 100hp six doesn't really output 100hp for very long, at highway cruise, it's what, 30? 40? hp? The problem is the heat builds up in the transmission, even a 300 - 400 watt space heater locked in a metal box will get oven-hot.)
You could probably work out the difference in miles/gallon manual vs. auto trans in terms of BTUs/mile and figure out the amount of heat produced in the automatic transmission that way.