Remote Trans Cooler needed or not?

How high is your stall?
How high does the oil temp get?
How much power are you making?
How often are you using it?
How hot does it get in your neighborhood?

Obviously the questions are all designed to get a handle on the oil temps.
Regular ATF likes to run around 160/180*F, but is fine to 210/220. Around 240*, it will start to give up, and if abused there, will cook your friction materials, thus turning color, and losing it's ability to lubricate. The color change is caused by the burnt stuff in it; and that stuff is too small to be caught by the filter; and while not as abrasive as sandpaper, it won't be doing the soft parts any favors.
Bottom line is that if your oil has not changed color, then it has not overheated, and your trans guts are still fine. How well the oil is still doing it's jobs of lubricating and cooling, I cannot say.
To that end, I would still put a temperature gauge on it,
or shoot the oilpan now and then with an IR gun,
particularly on a hot day after a good run;
or when slipping around in traffic.

IMHO that cooler, as installed in your car, is just about useless, being nothing but a heat-sink. You can make it functional by dropping it some, and closing the back-end and sides, to force ram-air to drop down thru it. However, it will be susceptible to clogging by dirt/gravel/road debris; so leave a lil hole at the back-end for stuff to ram on thru.

On a side-note;
I have run my 904 without a cooler, for several winters and late into spring, with no ill effects. But that engine was just a lo-compression 318 4-bbl with a 2800stall and usually 3.23s. Not ideal but, she was just my winter power-supply; and I have a good amount of experience rebuilding Mopar transmissions. And, I always have a spare or three, lol. and I always had all summer to freshen it, which was usually May long weekend to September long.

It's all about the heat, obviously; but lol.