last time when my cobalt did that it was because it was overheating. couple solutions is if this is the issues is that the fan doesnt kick in until the engine temps are over 223 degrees or so. i would either.
1. rewire the fan to another power source that provides constant current
2. trifecta...
dont worry about the side molding, most of the time if you get hit its from a truck in which case the door of the trucks will hit higher than the moldings so they are not doing there job
or you could check out a junk yard. look for SS cobalts, check under the hood to see what engine, if it only has rear damage grab the manifold, throttle body etc