Have you had any bad electrical storms?
You wrote, " Specifically, it will run at any temperature that the thermostat displays, and it will heat up the coils inside, and once the coils are an orange hot color." Turn off the power to the furnace. At the furnace control board find where the thermostat wires connect. Now disconnect the wire connected to the W terminal. Turn the furnace back on with the thermostat NOT calling for heat (thermostat set to below room temperature). If it still behaves as before (furnace runs and shuts off), you need a new control board. If the furnace does not start heating, then you have either a bad thermostat or a problem in the thermostat wiring between the thermostat and furnace.