A fuel-fired heating appliance comprises a fuel source, an air source, a chamber in which fuel and air mix, a burner downstream from the mixing chamber, an igniter proximate the burner, a heat exchanger, a blower and a flue pipe. An ambient air inlet may be defined by at least one of the outlet end of the blower and the flue pipe extending between the interior of the flue pipe and an area ambient to the flue pipe. A flow rate of combustion gas may be controlled to a level below a steady-state flow rate during appliance warm-up.