Impala Engine hot, A/C off
There are two typical issues that cause this message to appear:
1. The ECT sensor (or wiring) is open or otherwise defective, or
2. The inner seal on the thermostat is deformed, allowing coolant to bleed through when the thermostat is closed. This causes the car to warm up too slowly, and the computer throws an incorrect flag: "Engine hot, A/C off".
You should check/fix these issues in the following sequence:
1. Use a scan tool to clear the codes. If the ECTS or wiring is open, the "Engine hot, A/C off" message should return immediately. If so, replace the ECTS or check the sensor wiring for defects. However, if the code does not return immediately, this does not automatically mean the sensor is OK. The sensor or the wiring could be intermittent. But you should move to the next step first.
2. Check how long it takes for the car to warm up. If it seems to take longer than normal, this is an indication that the thermostat is experiencing bleed-through. If so, replace the thermostat. (This is much easier than replacing the ECT sensor.) Once you get the thermostat out, inspect the inner seal. If it has twisted out of position, this was your problem. Replace the thermostat, and use a scan tool to clear the codes.
Changing the thermostat is fairly easy, and it may be a pretty old piece of equipment anyway. I lost about a gallon of coolant, but this fixed the problem on my 09 Impala with 155K miles.