Ok, Im quickly becoming an expert on this issue. I have an 03 Tahoe LS (for sale btw) and a new to me 03 Tahoe Z71. My prob is front climate control, but similar enough to discuss here.
I bought truck on Tues, test drive fine, my through inspection, fine. On drive home, ticking noise from front. The next day the auto clim control decides to blow hot air at me on hot day. Turn off and start again, all fine, except ticking. I find an old tsb with the exact symptoms.
Today took it in to dealer to reprogram hvac. Still got ticking on way home, but havent had the hot air problem.
This issue is the blend door or the blend door actuator. For the front, this is under the glove box. I can feel the ticking when I touch the actuator. I'm going to the parts store tomorow to buy a new actuator.
Hopefully that fixes the problem, if not, I'll have the open the plenum cover and see if the door is acutally sticking (gears broken or something).
You guys are having issues with the rear blend door and/or door actuator. The door pivots to blend hot and cold air to get the correct mix. Yours appear to be stuck. You'll have go google the location of the rear blend door actuator to find it. I'd try replacing the actuator first.
Also, when my truck was in dealer today, he said my tsb was old and not in their system anymore, but he did have a tsb for the rear blend door. Check it out.
Good luck.