The first thing I would check is if the rear fan is working, without it you wouldn't feel anything from the vents. Next I would remove the rear trim panel from the area and listen and watch as the selector is moved to be sure the blend actuator is operating to select heat or AC. A quick test would be to select heat, does the rear unit put out HOT air at each speed? If yes then the blower is OK. Then just be sure the blend door fully closes. If those all work then the next thing would be checking to be sure the system has the correct charge (1.87lb or 850g) of R-1234YF. To do that I would have a qualified shop remove the charge and measure it, then recharge with the correct amount. To go with that I would check the operational pressures to be sure the compressor is functioning properly, these are because you state the front AC is "cool" not cold.
This may explain it farther.
https://2carpros.com/articles/car-air-conditioner-not-working-or-is-weak/
Some of the testing will require a dealer level scan tool that has security authorization to access the systems in the vehicle to enable it to check the network and control modules.
Try these and let us know what you find.
Aug 8, 2026 at 3:01 PM