A furnace system for a heating, ventilation, and air conditioning (HVAC) system includes a furnace controller configured to determine a rolling average furnace run time of the furnace system based on a plurality of previous run cycles of the furnace system. The furnace controller is configured to segment the rolling average furnace run time into a plurality of operational time periods, wherein each operational time period is associated with a distinct fire rate of a plurality of distinct fire rates the furnace system. The furnace controller is also configured to operate the furnace system to sequentially implement the plurality of distinct fire rates associated with the plurality of operational time periods.