Hello and welcome to Just answer.com, Super mechanic here. About your vehicle.
On the 2006, the A/C system uses an expansion valve in place of the orifice tube. It is on the HVAC module, however, there has been a service bulletin issued for the problem of non-cooling for it, which involves a reprogramming of the BCM.
Here is the location of it along with the bulletin, thanks
Bulletin No.: 07-01-38-005
Date: July 18, 2007
Some customers may comment on poor A/C performance or that the A/C does not get cold enough after a long drive.
Some of the possible symptoms of this condition are:
Blowing warm air
Reduced air flow
Mist/Vapor coming out of vents
The cause of this condition may be due to the evaporator core freezing up.
Fix It Right the First Time Tips
DO NOT replace the evaporator temperature sensor for this condition unless diagnosis proves it to be the root cause.
The sensor can be checked for proper function using the Tech 2(R). Check the sensor for volts varying around 2.3V to 2.6V. This data is within the BCMand is displayed in the accessory list. If the volts are near zero, check for a good connection at the sensor. Also, inspect the harness for possible damage. The sensor is located on the driver's side of the HVAC module and can be accessed from underneath the instrument panel by removing the closeout panel and OnStar(R) module, if equipped.
DO NOT replace the thermal expansion valve (TXV) for this condition unless published SI diagnosis proves it to be the root cause.
If AC components have been replaced or the refrigerant has been evacuated and recharged and no PAG oil has been added back into the system, it may have a reduced oil level. Please ensure that the vehicle has the proper amount of PAG oil in the system, as low oil level will contribute to the evaporator freezing up. To return to a nominal level of PAG oil, it may be necessary to flush the system. Refer to SI for flushing instructions.
The Tech 2(R) must have software version 27.009 or later.
Recalibrate the BCM with new software using the Tech 2(R) and following the procedure below. This updated software will control the cycling of the compressor clutch to prevent freezing of the evaporator core.
Install the Tech 2(R) to the vehicle and power on.
Turn ON the ignition, with engine OFF.
Build the vehicle.
Select "Body Control Module".
Select "Module Setup".
Then press "BCM Setup" soft key to execute update. When completed command state will change from "None" to "BCM Setup".