if you do it, go thru the drivers side first, and then the passenger side cooler.
the drivers side is the the oil cooler side, it's the hot side, what the coolent comes out of the engine at. then once cooled down across the fens the pass side will cool it lower than coolent temp sensor reading that's in the block. what the that temp actually is, you'd need a extra sensor to say. you could also wire in a toggle switch to run the fans at high speed if you needed them, the coolent thermostat would keep the engine from over cooling and you might get a bit more tranny cooling if needed. honestly don't know if what you're towing is enough the engine needs both fans on anyways.
I don't pretend to have any experience with tranny cooling with towing, the little I've done has been fine with my stock setups. my in radiator cooling experience is from the oil side, my car is notorious for hot oil Temps, 2 flying laps of the track and I was hitting 300 deg. 260deg is comfortable, 320-340 depending on the oil is basically baking it, I try to shut down at 300. my car had the optional front mount oil to air cooler, it couldn't even handle mountain road runs, I put a small good quality spal fan on the cooler itself, and that kept me under 300 on the roads. went to the track and 2 laps I was having to do cool down laps. I then had 2 options, the larger aftermarket cooler that's well over 1000$ setup, most guys have good luck with it. or I caught a few old threads with some info about the in radiator coolers working well for them, not many replies and mainly the same thing, oh it's inefficient, you'll add heat to coolent blah blah blah theory's, (never hard coolent temp issues even with stock rad and fan) but no where did anyone post about trying it and it failing. so I took the gamble, found top brand radiator on ebay from a wrecked zo6, (wasn't paying 1500$ for a radiator to test the theory lol) swapped it in and ran lines to radiator cooler first, and than since I already had it, I left the oem front mount with the fan on it.
well next track day, I completely forgot to turn the fan cooler on, but never was about to hit over 270deg and that was running 2 seconds faster lap time, mainly from being able to run longer sessions lead to driving harder, times came down and not worried about Temps anymore. except tires and brakes.
day did get cut short cause of a oil hose on a fitting didn't hold, so make sure what you make the lines with is proper rated. it was my fault, I researched the part numbers from the Parker catalog at work but then ordered it from a random Amazon listing by the foot (I should have ordered from our vendor, but they really only deal in 50ft or more orders) I never checked that they sent me what ordered till after I got it home from the track, checked the numbers on the left over hose and it wasn't what I wanted. the temp rating wasn't high enough to have headroom for the hot side oil. must have been really hot before being cooled. the temp sensor is in the sump. it's much hotter as it exits the pump from being compressed. I'd guess tranny fluid would be the same, if you took a temp reading off the converter outlet, it would be pushing the limits of the fluid.
anyways, it can't hurt to try, if it doesn't work you'll already have the hoses and fitting made up for a big from mount cooler. there's a long 20plus page thread around there about it. worth a read if you can find it.
