Er, only coolant flows through the radiator and the engine block for cooling. Some more exotic cars have oil coolers, but I’ve never heard of any car w/a transmission fluid cooler!
I have seen transmission casings w/cooling fins however. But this obviously requires airflow… Fortunately, the amount of heat generated is nothing compared to an internal combustion engine (some of which are designed for airflow cooling only).
My knowledge only really covers manual tranny’s, so I apologize for not contributing anything more useful.
Some of the older cars seemed to have problems with overheating when idle. However, on most modern cars I’ve driven, the temperature gauge doesn’t creep up at idle at all. With electric cooling fans, modern cars don’t have cooling problems standing still. Or at least they shouldn’t. If you do have enough heat buildup that you’ve got to worry about the transmission, you’ll see the gauge hit the hot range while idling, or even have the coolant boil over… and you’ll have a lot to worry about besides your transmission.
I realize this is GQ, not IMHO, but my solution to the “should I/shouldn’t I” debate is this: at stoplights or the like, I leave it in drive, because I don’t see the logic in shifting the automatic for such a short period of waiting. When I’m sitting for a long time, such as while waiting for a long train at a crossing or when the person ahead of me at the drive-through seems to be ordering that a live cow be brought to her vehicle and slaughtered so that she can tell how fresh her hamburger is, I put it in neutral. It’s mostly just because I get tired of pressing down the brake, though. YMMV.
Randy, manual transmissions generally don’t circulate anything to the radiator - probably because they don’t slip as much. Automatic transmissions, however, almost always have a pair of hard lines that run transmission fluid (not engine coolant) to a cooler in the radiator and back. This seems to have been around almost as long as automatic transmissions; my '66 Dodge Dart uses this sort of setup for its TorqueFlite 904 automatic transmission.
the issue is whether the shifting into neutral itself wears more than the torque converter sitting there working. i’m not sure which is worse, neutral might be a good idea because it takes strain off TC but leaving it in makes for less shifts in the transmissions’ life. i would venture to say leave it in for anything under 3-4 minutes, after that shift into neutral.