some older models had a fan/limit control utilizing one sensor, a helical coil comprised of two strips of dissimilar metal laminated together. the sensor protrudes into the cabinet and resides next to the heat exchanger so it is affected when the heat exchanger heats up. as it heats up, it tightenens, causing movement on a wheel with cams. if you have this, the part you see is a rectangular control with a metal cover. two thermal switches are inside, one to control the fan and the other to control the gas valve. when you remove the cover, you see four or more wires going into it and a silver metal dial. this dial contains three setpoints that are adjustable; fan off, fan on and limit. the max limit setting is 200 degrees and will disable the gas valve if the temperature exceeds the setting. the fan settings are adjustable to compensate for the fact that the coiled sensor becomes weaker over time. back in the day, many service calls were generated because the fan would not shut down. a slight adjustment of the 'fan off' setting would remedy the problem. we would also adjust the 'fan on' slightly lower too. as pointed out, air moving across the heat exchanger is essential, but typically, the heat comes on first, then the fan. the fan goes off last to finish cooling down the heat exchanger.
note - if you have this type of control, you have a very old furnace and you should thoroughly inspect and test the heat exchanger for cracks and holes.
question - do you have a metal box hanging off your furnace that your flue pipe connects to *