Air condition

Temp gauge for instrument cluster or the dash or the climate control unit itself? If it's the climate control unit then that might be the issue causing the fault.

First check to make sure freon is in the system compressor clutch will not engage if system is empty.

An overcharge or undercharge of refrigerant in the system will trip the pressure safety switch which cuts power to the compressor clutch. The compressor relay could be bad. Or If the high or low pressure safety switch is stuck then it will not allow the clutch to engage. To check system pressure: Only use an automotive a/c manifold gauge set. The cheap ass ones that come with those diy recharge kits like a/c pro hardly ever give an accurate reading. Also to actually know the system is over/under charged you need to measure the suction line (low) and the discharge line (high) at the same time. Operating pressures should read approximately Low: 35psi and High: 200psi depending on outdoor air temp. Since the compressor clutch wont engage you can take a static pressure reading. Typically it will read about 45psi on high and low side. If there is no pressure then that shows there is basically no charge. But static readings will not show you if the system is overcharged because 1 ounce of refrigerant will have the same static pressure as several pounds. To check relay: Locate relay With a voltmeter check for current (DC) across the relays coil by measuring from terminal 2 to 4 on the relay. If there is no current then relay and fuse must be replaced. If you do get a reading then move on to measuring across terminal 1 and 3. If no current then replace relay and fuse. To check the pressure switch: Locate the high and low pressure switches With a voltmeter, check to see if there is current across the switch. If there is no voltage across the switch then it might be stuck open and need to be replaced. If all of the above are good then the clutch should engage. If it does not, then make sure the wires for the compressor clutch are not corroded and have good solid connection. After that if it still does not engage then the compressor clutch coil is burnt out.