It is unlikely to be the thermostat. More likely this is a restriction in the system or a pressure issue.
Most all A/C issues are related to the pressure in the system, so we need to start with this.
https://www.2carpros.com/articles/re-charge-an-air-conditioner-system
Once we confirm the pressures are correct then we can move onto a possible blend door issue.
https://www.2carpros.com/articles/replace-blend-door-motor
I highly system if the rear AC system is working correctly then this is a door actuator issue so I would suggest removing it and moving the door manually and see if the operation works correctly and blows cold.
If it does, then just replace the actuator and retest the system.
I am attaching the process below. Please let me know what questions you have. Thanks
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Wednesday, December 15th, 2021 AT 2:34 PM