I've never had an issue like this one. I did a little checking on the climate control unit. The temperature sensor was full of lint and debris so I cleaned that out. Removed the unit from the dash and removed the fan from the back that draws the air over the sensor.

The data on the temperature sensor before the cleaning was -27 degrees F and after is -40 degrees F. I suspect that the sensor is broken.

The sensor appears to be an integrated part of the climate control unit. Has anyone ever changed the sensor itself?