I usually tow in summer up 6% grade with a 24' Toybox. It's 7200lbs empty so it's probably 8000lbs for camping. I only have problems when I tow up the hill at too high rpms. I just slow down and the engine temp come down. I'm waiting on Stillen new radiator and thinking of adding the stillen aux radiator.
There was a recall for some 07's with bad wiring to the electric fan; that could cause problems when towing if you haven't had it fixed. And I'd agree with keeping the transmission in lower gears under load to help it stay cooler.
My '06 CC 4X4 LE ran a little hot in 07/2006... it was 116° and we were heading up the Baker Grade into Las Vegas with a 23' Fleetwood Nitrous HyperLite. The total weight was about 13500lbs for both the truck and trailer (had it weighed in Utah, 6800 for the truck and 6300 for the trailer.)
Anyway, I had the A/C on and was only doing about 40MPH and the engine temp went up to the 3/4 mark line. It never went past that mark... Turning off the A/C brought the temps back down.
I later found that the radiator cap was dripping some coolant, as if it wasn't tight enough. It could have been pressure related? The cap was replaced under warranty.
In 04/2007 I did the same trip, was a little lighter and running the Baker Grade at 80° at 65MPH with the A/C on, the temp gauge never moved off normal.
The trans has always remained cool even when towing up some awfully ugly hills in CO during July.