I'm not totally familiar with your particular unit, but it sounds like the heat relay has its contacts stuck closed. You refer to it as an air conditioner with heater and not specifically a heat pump which is what led me to the above suggestion.

my air conditioner with heat. when the heater is on, it will not shut off after reaching temperature input. I pressed the reset button on the plug in on the wall,the heater stays on. when I press the power button off the lights go off but the unit still runs with hot air flowing. I have unplug the unit any help is appreciated. it is a Frigidaire 25,000btu cooling and 16,000 btu heating