I don't know all the facts about electric fans, but they turn on and off cycling air through the radiator to cool down the coolant fluid. I know the fans are supposed to stay on for a few minutes after you power down the vehicle to reduce engine temp.
Your thermostat is what I would point at. It contains a wax type pellet that moves up and down when engine temps change. It has no electrical circuits attached and will not throw any CEL's if the pellet is stuck in the open position (on). I have seen some pellets destroyed into a bunch of pieces. When its in the closed position, coolant will not flow and fan will be not turned on.
The SAS or airbag light may be stuck on the on position if a crash sensor is not functioning properly or has been damaged. You would want to take that in to the dealership soon for service. Or you can with your scan tool, look up BCM codes if its a sensor.
The a/c could be low on Freon which is common. Another could be the a/c compressor clutch can be stuck as well. When you turn on the a/c, turn off all accessories to hear the clutch engage between each mode (1,2,3,4, off), if you hear it make the "click sound" then the clutch is good and be sure to have a spotter look at the Y shaped clutch on the serptine belt, ensure the spotter sees it go from stop (off) to spin (on). More than likely, you should be just low on Freon if a/c blows warm, since cobalts don't have cabin air temp sensors. Just a front sensor for atmospheric air temp.
2009 Cobalt LS XFE U74
Mods: K&N Typhoon Intake, Option Cat-Back Exhaust, Cosmo Short shifter, Maxxim Ahead 17X7's, MPx shorty antenna, FE5 Strut/shocks, Tein S Techs, Moog endlinks, Moog spring seaters, ZZP shorty header, LSJ downpipe, LNF front grille