I just saw your questions about the rh32 swap, sorry for taking so long to get back to you. I'm sure you figured it out by now but just in case.
I used a 98 computer on my 97 with no issue but I cant guarantee that yours will work.
I used an external cooler from advanced auto connected to the factory tranny cooler lines. The check valve keeps all the fluid from draining back into the pan once the Jeep is off. My check valve is bad so if the jeep sits for a long time I put the tranny in neutral to build fluid pressure before tring to shift into gear.
I'm trying to do the same transmission swap that you did. I have a couple of questions if you dont mind. I have a 2001 tj and found a 32rh out of a 98 tj. The guy I got it from gave me the computer out of the 98 auto. Will that computer work on my 2001? Also how did you cool the transmission? I am planning on using an external transmission cooler. Do you know if I need to get the factory cooler lines? I read that they have some kind of valve that the transmission needs to work properly. Or can I just run regular lines from the transmission to the external cooler. Any advice you have would be greatly appreciated.