1971 D615MH Coleman Furnace,
Sounds like a stuck relay or a bad control board at the furnace end; or a short in your thermostat wiring. You could try disconnecting the thermostat wiring at the furnace end. If it still runs with the thermostat disconnected entirely, you're looking at a stuck relay or bad control board.

If it doesn't run with the thermostat disconnected, check for shorts in the thermostat wiring between the furnace and the thermostat. You could do this with a multimeter. If you don't have a multimeter, try removing the thermostat from the wall and connecting the thermostat to the furnace with short length of wire. If the system behaves properly with the short length of wire, then you've isolated the problem to the thermostat wiring between the furnace and the thermostat installation.