Amazing that OP asked about "fan control' and gets a thermostat procedure. :rolleyes::rolleyes:
Anyhow :
Combination Fan & Limit Control: This control turns the furnace blower on and off at the proper times. The FAN ON setting on this control makes sure that the blower fan does not turn on (even though the building thermostat has asked for heat) so that the furnace wont' blow cool air into the occupied space.
Furnace FAN ON: When an adequate warm temperature has been reached inside of the furnace warm air plenum chamber the FAN ON switch turns on the furnace blower to deliver warm air to the occupied space.
Furnace FAN OFF: The furnace combination fan and limit control FAN OFF setting lets the furnace blower continue to run for an interval after the furnace burner has turned off, but will shut the blower off after the heat exchanger has been cooled down and the heat it contained has been sent to the occupied space.
Furnace LIMIT: The LIMIT indicator setting is a safety control that will turn off the oil or gas burner if temperatures inside the warm air plenum exceed a safe level.
When does the furnace blower turn OFF in normal operation?

When the thermostat has been satisfied and turns off the oil or gas burner at the furnace, the fan limit switch will cause the blower or fan unit to continue to operate until the temperature at the supply plenum has reached or dropped below the "cut-in" or "fan-on" lower limit on the switch.
When does the furnace oil burner, gas burner, or other heat source turn OFF in normal operation:

On most heating systems the burner or heat source will continue to run all of the time that the building thermostat is asking for heat, and will stop running as soon as the thermostat is satisfied. If the furnace oil or gas burner is very high capacity, or if the furnace fan/limit controls have been set to cause this effect, the burner may on some systems cycle on and off periodically while the warm air blower continues to run.

It seems like your Carrier Day & Night Furnace is experiencing ignition issues, leading to prolonged heating cycles and cold air blowing into the house. To address this, you may want to check the flame sensor for dirt or corrosion, as a clean sensor ensures proper ignition.

Additionally, inspect the gas supply and pressure, ensuring it meets the furnace requirements. Check the air filter for blockages, as a dirty filter can affect airflow and heat distribution. If these steps don't resolve the issue, it's advisable to consult a professional technician to thoroughly assess and troubleshoot the furnace for more complex problems that may require adjustment or replacement of components.