I don't haul much stuff but this 94 3.9 I have was a commuter rig down around San Bernardino area for about 16 years and it has only ever been connected to the radiator cooler since I have owned it and afaik that is all it ever had. That is the very hot area out east of LA in SoCal. The trans it had was original when I had it rebuilt.
My motor does get hotter than I like in Summer since I bought it, so I went with the 180 thermostat instead of the usual 195.

 

Alright sorry guys it's been a minute. I installed the new cooler and routed the lines through the radiator, then through the new cooler, then back to the transmission. I flushed out all the old fluid and put in a bunch of new Valvoline Max-Life Multi-Vehicle stuff.

On top of this, I installed a transmission temperature gauge from GlowShift and used one of their pillar pods, and it looks pretty good! For the sensor I used one of the test ports on the transmission.

So, I took it for a drive and it went... interesting. 1st and 2nd shift just fine, but when I try to get to 3rd, it hesitates up until 3500 RPM when it finally shifts. It is not a hard shift either, it's just a very late one. From there, it will not downshift back to 2nd whatsoever. It will continue to stay in 3rd unless I put it in neutral and back into drive, where it goes to 1st and the process repeats.

During my test drive, my temperature gauge only read about 120°F, which seems awfully cold, when it should be 175-215°F. Maybe installing a secondary cooler on top of the primary one was unnecessary? Maybe I should've just routed it through the radiator?

The new hypothesis is that the fluid is too cold for 3rd gear to engage quickly. The new solution is to install a switch valve that will toggle between the fluid cycling to the secondary cooler, and the fluid going straight back to the transmission, from the radiator. That way, during summer, I can put the secondary cooler on and keep it cool. Do you think this will work?

 

The make thermostatic valves for just such an occasion. Put it between the radiator cooler, and the aux cooler. There, it will allow the fluid to warm up quickly, but, if it starts getting too warm, the aux cooler will kick in, and you don't have to lift a finger.

Being an older trans, the first three gears are purely hydraulically controlled. Sounds like your governor might be sticking, or, the TV cable needs adjusted. (check for binding while you are playin' with it.)

 

How much are those? Can I set it to switch at about, let's say 180°F, or do I have to buy one with a pre-set temperature?

 

Here is one that is 180*, found 'em on amazon as well, for like 50 bucks.

 

For some reason this thread popped into my head this morning. I do not remember anyone making mention of the ATF fluid you used. I suggest you read this link from the top section of the FAQ page (Fluid Change) and follow the two links at the bottom post #10 https://dodgeforum.com/forum/1st-gen-dakota-tech-66/
Maybe the diagnostic link next to it on the FAQ page may help as well. Anyway if you are not using ATF 3 or 4 that could be your problem with overheat.