Methods and related systems for operating a furnace are disclosed. In an embodiment, the method includes activating a burner assembly and a first fan of the furnace to combust fuel and air and circulate combustion gases along a flow path extending through a heat exchanger of the furnace. In addition, the method includes operating a second fan of the furnace to circulate air across an external surface of the heat exchanger of the furnace and produce a conditioned airflow. Further, the method includes monitoring one or more parameters of a motor of the second fan indicative of an airflow rate of the conditioned airflow, and deactivating the burner assembly, whereby combustion of the fuel and air in the furnace ceases, in response to the one or more parameters indicating that the airflow rate is less than a minimum airflow rate.