There's two actuators in the rear - one for airflow mode and one for temp. Assuming you get good hot coolant flow to the heater core back there, you have a bad or failing temp actuator.
I've posted the exploded parts view of this area before, which you could find in a search. You have to remove the passenger side rear interior panel, poke about and feel for hot coolant hoses going to the heater core, and then observe the actuator move from end to end as you fiddle with the rear temp control.
If you have access to a trusted GM-experienced mechanic with a high end scan tool, they should also be able to talk to the HVAC control module and see if the actuator is following its commands.
I've posted the exploded parts view of this area before, which you could find in a search. You have to remove the passenger side rear interior panel, poke about and feel for hot coolant hoses going to the heater core, and then observe the actuator move from end to end as you fiddle with the rear temp control.
If you have access to a trusted GM-experienced mechanic with a high end scan tool, they should also be able to talk to the HVAC control module and see if the actuator is following its commands.