OP has a half-ton Denali. I have a 2500.
A 2500 should pull your trailer with no issues whatsoever. And there's no need to get a second transmission cooler. Dex VI fluid can handle much higher temps than older fluids. 200° is normal operating temperature after 30-60 minutes of driving. The "transmission hot idle engine" warning only comes on at 265°. I never got higher than 241°, and that was with a GCW at 16,300 lbs driving up to almost 10,000-foot altitude, with the A/C running.
The 2500 Suburban/Yukon XL are actually "sleepers." Because they share the same body as the half-tons, everybody thinks they're the same, but just beefed-up a little. The truth is that under the shared body is a completely different truck - bigger/thicker frame, bigger axles, bigger brakes, heavier-duty transmission, different/more-durable engine, heavier-duty suspension. They're completely different animals from their wimpier, half-ton cousins. You've made a great choice upgrading to a 2500. It will serve you well for many years and miles. Mine is at 170,000 miles and is still PERFECT. I've spent exactly $23 in repairs over the last three years, all the while beating the snot out of the truck.