you can check the rear hvac in different ways
1. reach under the passenger rear side behind the rear wheel there is 2 hoses going up into the rear heater core, after a drive and the vehicle is at normal operating temperature then BOTH hoses should feel warm. if one is warm and the other cold then it's possible the heater core is clogged
2. if both hoses are warm, then it's likely the rear blend actuator is defective and is simply stuck on cold (by far the most common problem.)
3. remove the passenger rear inside kick panel that covers the rear hvac unit, visually check the actuator (there are 2 actuators) 1 is for roof/floor the other is for hot/cold. the one closest to the blower motor is for hot/cold, the actuator has a slot in it and 3 position indicators, when you adjust the heater control from hot/cold or anywhere in between then the actuator should rotate, if it does not rotate then it's probably gone bad and needs to be replaced. if both hoses are warm and the actuator rotates then its possible the blend door has broken inside the hvac housing.
search youtube for instructions & video on how to access the rear hvac unit, the process is the same from 00-14 for all gm suv's