A furnace for heating air includes a primary heat exchanger and a secondary heat exchanger to transfer heat from a flow of hot gases, the secondary heat exchanger being arranged downstream from the primary heat exchanger. A collection/discharge box fluidly couples an outlet of the primary heat exchanger and an inlet of the secondary heat exchanger. An enclosure houses the primary heat exchanger, the collection/discharge box, and the secondary heat exchanger, and includes an air inlet and an air outlet. A main air flow path extends through the enclosure from the air inlet to the air outlet, and the primary and secondary heat exchangers are arranged along the main air flow path. An air bypass channel is arranged to be fluidly parallel to a section of the main air flow path, and the collection/discharge box is arranged along the bypass channel.