I have an 06. Tow with the tow button in.
Shift it yourself and keep it out of overdrive (6th gear)
Shift down to the next lower gear at 2200 RPM.
Get an EDGE or a EFI tuner, Edge is the safest bet for towing.Run in TOW mode. Install it and a Pyrometer probe and you can then, more accurately, observe water, transmission and exhaust temp.
The fan should come on at 220 and run until temp is below 215.
They are big with a lot of blades so they are noisy.
Buy a set of Parker transmission cooler lines and replace you lines as they are the worst design in the world and you'll find puddles in your drive.
http://madjackdiesel.com/allison-1000-transmission/parts-pans-etc/diesel-race-parts-transmission-cooler-repair-lines-2004-5-lly-2010-gm-duramax-pick-up-trucks.html
A pump rub kit. http://www.merchant-automotive.com/transfer-case-pump-upgrade-kit.aspx Read up on it.
Then buy a pair of Timken fron hubs so when they go out you'll have the good ones as Chevy hubs last about 50K miles. Best economy is 65MPH towing.