Are you locking out overdrive? Watch your tachometer and see what is happening. First, take note of what RPM the engine runs at normally on the flats at your towing speed, without the trailer. Then, monitor the RPMs with the trailer. If they frequently climb about 500, that is a sign that the unlocked torque converter is letting slippage take place, and this generates a ton of heat. Or if you see that the RPMs climb about 800-1000 to help the truck gain speed, then drops down (and the truck loses some speed), then the RPMs climb again, this tells you that the transmission is shifting back and forth too frequently and this generates a lot of heat also. Solution: lock out overdrive while towing, and see if this solves your heat problem.
The other question is, how fast are you towing? 65? Maybe faster than that? If so, you may just need to keep it down to 60 mph. Wind resistance increases exponentially with speed, so 5 mph reduction can make a big difference.
If you already have an aux tranny cooler you should not need another one. But check these things:
1. Are the cooler's fins dirty?
2. Did they route the tranny fluid lines correctly? They should go to the normal cooler AND to the aux cooler (first one, then the other), not just the latter. I have heard of screwups where they routed the lines wrong. Rare, but possible.