To substantially reduce inequality in hot combustion flow rates through first and second heat exchanger tubes from a fuel-fired heating appliance burner box connected thereto and internally combusting a fuel/air mixture received therein from a source thereof to create the hot combustion gas, a perforated diffuser member having a non-uniform perforation pattern is provided. The fuel/air mixture is flowed through the perforated diffuser member into the interior of the burner box. The non-uniform perforation pattern of the diffuser member functions to alter relative combustion gas flow rates through the first and second heat exchanger tubes in a manner reducing an undesirable operating temperature differential therebetween.