I have a 09 chevy cobalt and when I have my a.c. on in the summer and I'm going a low speed or stopped my car hugs and feels like its going to die. Help?

Chugs*

Sounds like the compressor might be failing and adding extra load to the engine.

I have 2010 Cobalt LS coupe I noticed the other day driving in Florida weather, not that hot mind you but after a short day of driving the temperature picked up from 195 to 210 quick. The idle for the engine had a slight slow rev up and down. It sounded somewhat putt putt. Later that night after being off for a few hours, then having a short drive by the time the car was home it hit 208. I let it run for about 10 minutes where it hit 218 and the second fan kicked in and brought the temperature back to 180 in the garage on a cool night. I will see where and if the idle shows issue along with the quick heating. All I've been told about the car is it is run completely on sensors and electronics that indicate issues. Without a problem light to indicate a problem, there is "nothing worth looking at" to Chevrolet.