For a couple of winters now, my furnace will not turn off all the time when I turn the thermostat down or it will just keep running forever above the set termostat temperature. The airconditioner works fine with the thermostat. The thermostat was replaced last year to see if that would solve the problem, but it did not. Even after I turn the heat to off, and then turn off the circuit breaker, the heat keeps running sometimes. Then I have to turn off the furnace fan to get it to stop. Or, sometimes, if I turn the thermostat to OFF, then to COOL, then back to OFF, the heat will stop running. Since the termostate responds correctly to the air conditioner, and also since the termostat has been replaced and still the heat keeps running above the set temperature, what could the problem be? It used to be intermittent, but now it happens about 8 times out of 10. So, once in a while, it will work right, but not very much. Thank you.

You have a short in the thermostat wiring.

What can be done to turn it off?

Turn off the Breaker.
A Tech Might remove the Heat wire from thermostat, if heat goes out, it is at the thermostat, if it doesn't go out, it is the wiring, or a relay stuck.