there are too air temp actuators that move the doors in the heater box
if the low side line going through the firewall is frosty and it is pushing heat
you need to verify these actuators are moving when you change the temp control
click here to view page 1 of the wiring schematic
click here to view page 2
you need to check the left temp door actuator
1. Check for Left Mix Door Actual, and Air Mix Door Left Commanded on the scan tool when the temperature changes on its own.
2. Check the right I/P junction block located under the dash on the right side, connectors C4/X4 & C5/X5 for poor terminal tension, backed out terminals or connectors not fully seated.
3. Check the actuator connectors for poor terminal tension, backed out terminals or connectors not fully seated.
4. If no wiring issues are found and there is still a concern with an HVAC actuator, before replacing the actuator perform a reset of the front HVAC control head. To perform a reset remove the "HVAC BATT" fuse for one minute and reinstall. After the fuse has been reinstalled start the engine and allow it to run for one minute without using the hvac controls. After one minute use the Tech 2 to perform a door relearn procedure by entering Body/ HVAC Control Module/ Special Functions/ Recalibrate All Motors. If the actuator begins to operate, no further repairs necessary. If the actuator still does not operate perform normal diagnostics, by first checking for any new DTCs.
there is a relearn that can performed on the unit with a scan tool
click here to view the left actuator image
you can try removing the actuator and moving the door manually to see if it cools. if it does the problem is with the control unit or the actuator
let me know how you make out