there is a bypass on the side of the trans, that if open, will bypass all fluid to the cooler lines. that bypass is there so if the cooler ever got blocked for some reason, it would insta-burn-down the trans from no fluid. in essence, it goes from the outlet port, right back into the trans. if the bypass is the issue, you need to figure out why the bypass happened. i believe i read mark state that bypass failures were rare. if the bypass opened, it opened for a reason.
but it will do just what your having happen. heat up the trans fast, as the fluid never leaves it.
and what tony was saying, you moved the old trans to a new truck and the problems didnt follow. great. move the old cooler to the new truck also, see if the problem follows yet. if it does not, you have other issues. if it does, there, fix that. currently your putting a new cooler on it, without knowing for sure if you need one. you could be putting the new cooler on it, just to go, damn, thats not the issue after all.