I didn’t think that these cars had one, they just use flaps to blend HOT and COLD air to achieve the set temperature.
Maybe it is just a temperature flap motor that has failed, these flap motors do tend to fail.
Try demanding Hi wait a minute, then demand Lo and wait a minute, repeat maybe 10 times, doing that might clean up the positional feedback track enough to allow it to work for a “while”. If not it is really failed or another issue.