Intermittent error message "A/C off due to high engine temp"

I'm seeing this intermittent message on the display, "A/C off due to high engine temp". The car listed above is non turbo. I've had the car for 5 months. Car is in good overall shape. The dealership is fighting me on repairing this error code. I've done some investigation online, and see that this has been an ongoing problem that General Motors has been aware of for several years. I haven't found any resolution posted online, of the way to eliminate this problem. It appears that this code can be potentially caused, by several components. I've heard that the BCM, (Body Control Module), could be the main issue. The thermostat, and two sensors that control the flow of coolant, and the wiring harness that supplies the BCM. Symptoms are when this code appears are the temperature gauge on the dash starts moving back and forth wildly and erratically, and the error code appears on the display on the dash. Also, it appears that the air flow from the defroster vents is reduced, as well as the temperature lowering of the air coming out of the defroster itself. My question is, can someone please inform me of all the parts that could be potentially involved, in repairing this error code? When this is fixed by the dealership, I don't want them replacing one part randomly at a time, causing me to make multiple trips to the service repair garage, to fix this problem. The salesman says that he will take care of getting this fixed for us, but, I find it difficult to trust him, since GM knew of this issue for years, and has failed to recall cars for this problem. We are going to take a video as this problem occurs, (since it's intermittent), the next time it happens, to prove to the dealership, that this is happening. If we take it in without proof, and the mechanic does a diagnosis, and the code doesn't come up, they won't do anything to fix this. Can someone please help? Thanks, and sorry about the length of this post, just a lot of information.