im not familiar with toyota automatics... haven't seen many of them.
but they are no different than any other when it comes to cooling, get a B&M 70264 cooler, take one of the factory cooler lines and add this cooler in line with the factory cooler (or run it standalone even)
MY question would be why would the transmission care if the t case is gear or chain drive?
because when swapping in a gear drive unit he looses half or more of the trans/tcase volume of fluid.
a very LARGE cooler would be best
