2003 Chevy Tahoe Rear Blower

If I am understanding correctly, the rear blower works as expected, with front or rear controls. The temperature cannot be adjusted with either control panel, it is defaulted to cold. This assumes also, that the front HVAC functions normally. There is on bulletin that may apply, it involves a possibly binding temp door.
#PIT4226A: Rear HVAC Temperature / Mode Inoperative With DTC B0429 Or B3531 - keywords actuator bind control cold door head heat hot motor move no stick stuck valve warp wire - (Jan 5, 2009)

Subject: Rear HVAC Temperature/Mode Inoperative With DTC B0429 or B3531

Models: 2003-2006 Cadillac Escalade, Escalade ESV

2003-2006 Chevrolet Suburban, Tahoe

2003-2006 GMC Yukon, Yukon Denali, Yukon XL, Yukon Denali XL

This PI was superseded to add additional note that a low battery can cause this concern. Please discard PIT4226.

The following diagnosis might be helpful if the vehicle exhibits the symptom(s) described in this PI.

Condition/Concern:
Owners may comment that the rear HVAC temperature or mode door will not operate. When checking for DTCs a B0429 or B3531 will be present in the "Rear Aux. Climate Module". This DTC will set if the mode or temperature door is stuck.

Recommendation/Instructions:
Note: Before reviewing the procedure below, make sure the power and ground connections to the "Rear Aux Climate Module" are ok and that the battery is ok. Reports from RSE's in the field have found these codes to set when the battery is at a low state of charge or the battery has failed. Please check the battery with the Midtronics tester before proceeding below.

Remove the affected actuator and manually check the affected door for a binding or stuck condition. If the door is binding or stuck, replace the affected door.

Note: Currently on short wheel base utilities (Escalade, Yukon, Tahoe) the temp/mode doors can be ordered only as part of the upper HVAC case assembly. Utilize the parts department to determine the correct part(s) and the most cost effective way to repair the vehicle.

You can approach it a couple ways, first try removing the HVAC/ECAS in the underhood fuse block, and the RR ECC fuse in the left I/P fuse panel. Reinstall them after a couple minutes. This will initiate a recalibration of actuators on the next ignition cycle. Don't press any HVAC buttons for a few minutes or it may not complete properly. Check and see if it operates. If it does, it probably has a fault code that is setting, causing it to default cold. This is usually due to an overtravel of the actuator due to a faulty actuator, or somthing in the case that has allowed the door to move beyond stored limits. This may not correct the condition, or correct it for some time. If it goes to normal function, roll with it until it faults again. Otherwise, you may need to seek a scan tool that will communicate with rear HVAC and see if there are DTC's. If you do perform the inspection that the bulletin illustrates, and the door moves freely, I would consider replacing the actuator. When/if you replace the actuator, it would be advised to perform that recalibration mentioned previously.