err...well the name seems to say it all "Transmission Cooler". It takes the fluid from the transmission and cools it exactly the same way the radiator for your coolant works. Heat is a big enemy of any transmission and the cooler the better
Yes. Even your engine coolant will benefit. Normally, the trans fluid passes through the radiator. That heat from the ATF prevents the coolant from cooling off as much as it could. Now install an aftermarket trans cooler, and pre-cool the atf before it enters the radiator. You also get a cooler running trans, which tends to keep the engine running cooler as well.
All benefits gained are cooling, but it affects the cooling in several ways.