Hey! Welcome to the forum. Have you checked for the radiator any leaks? Check upper and lower radiator hoses, especially upper leading towards the backside of the block driver side (thermostat location). You can also have a pressure test performed where they test for proper pressure in the system to determine if a leak is present.
If you were to have headgasket issues, look at your color of your coolant reservoir fluid. If it looks like chocolate milk then oil is present. Another telltale sign is to look at your oil cap and inspect the underside of it..if it looks like coolant, then that's a pre sign.
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