Engine hot A/C off message

My car had said engine hot A/C off for some time now. Went to a mechanic shop. They said it was the water pump and the thermostat also needed a new battery. Got that changed, still reading the same. As I went back the second time it turned off as soon as I turned in. Nothing. Drove fine for a while. It came back on and I took it back, they told me that it was some kind of wiring issue. They re wired some stuff because the engine melted some wires. Got that done. Still came on. Brought it back and said it was probably a blown head gasket. Said the fans weren’t turning on and they flushed the radiator. And that there was nothing else they could do that it “could” be a blown head gasket. Not to take it back. So I’m out of options.