If you try to start the car when the temp is high, will it start? How quickly will the gauge go back to normal if you ignore the apparent overheat and start it? The temp sensor may be in a spot in the engine that gets pretty hot after the engine is shut off and there is no coolant flow. This may be normal behavior for this vehicle. I don’t think there are any Chrysler products built in the last 15 years or so that let the fans run with the key off.