I did miss state John,
Actually the heating cycle is this, Thermostat calls for heat, Burner starts, when fan /limit control reaches a pre set temperature the blower starts, when the thermostat contacts open , when the room temp reaches the set temp, the burner shuts off and the fan continues to run until the fan limit senses the temp has dropped below a set temp, to protect against the temperature going above the set temp, the thermostat is usually equipped with a tiny heat anticipator heater, this warms the thermostat so it actually turns off a degree or so before the room temp is warm enough, then the residual heat in the furnace, considerable in these heavy old units, brings the temperature in the room up to set temp, preventing overshoot.