Why do I have a Engine hot A/C off message

If the engine isn't actually overheating, it could be a bad temperature sensor being read by the computer. So if you knew enough about cars to be properly definitive in your question, we could properly advise. This is better left to professional mechanics who can actually see the car.

Well your first mistake was going to a quick lube place. You need to have a reputable shop look at it. Sounds like the coolant temperature sensor is unplugged or has failed. When the computer loses the signal from the coolant temperature sensor it assumes the engine is overheating. To try and prevent serious damage to the engine the air conditioning is disabled and the radiator cooling fans come on at high speed. Hope that helps! Jim