1. Measure the temperature around the cabin temperature sensor.
2. Measure the resistance between terminals of the cabin temperature sensor.

Cabin temperature sensor removal/installation
Evaporator temperature sensor removal/installationMazda 6 Service Manual: Turning the Engine Off
WARNINGDo not stop the engine while the vehicle is moving: Stopping the
engine while the vehicle is moving for any reason other than in an emergency is
dangerous. Stopping the engine while the vehicle is moving will result in reduced
braking ability due to the loss of power braking, which coul ...
Mazda 6 Service Manual: No.8 no cool air
When performing an asterisked (*) troubleshooting inspection, shake the
wiring harness and connectors while performing the inspection to discover
whether poor contact points are the cause of any intermittent malfunctions.
If there is a problem, check to make sure connectors, terminals ...