Will a DTC be triggered when the DIC reads "A/C off"?

Question

The message is telling me the A/C is disabled due to over heating but the message and the over heating are wrong. What I want to know is whether a code is stored and if that code will tell me where to look to find the screw up (temp. Sensor, temp. guage, wiring, etc).: Any help will be appreciated Oh by the way the message comes and goes and when the message is on, the temperature guage does not register (shows cold,).