I'm not sure HOW that would work, having two sets of cooler lines hooked up to the same transmission? My car does NOT have OEM style lines hooked to the radiator.
That's your ONLY transmission cooling? Yikes!
You cannot over cool an automatic transmission, but the one of the things that will kill it pretty quick is heat. With very little air flow through yours I would question how effective it is.
If it were me, and it will be soon because my car is getting a new trans, I would get a stacked plate cooler and put it in front of the radiator. The finned coolers like yours are ok, but just ok. Stacked plate are more efficient.