Method of operating a heat exchanger (100, 200) presenting: • a first gas inlet (111, 211), a first gas outlet (121, 221) and a first gas flow path (110, 210) extending from the first gas inlet (111, 211) to the first gas outlet (112, 212); • a second gas inlet (121, 221), a second gas outlet (122, 222) and a second gas flow path (120, 220) extending from the second gas inlet (121,221) to the second gas outlet (122, 222); the first flow path (110, 210) being in thermal contact with but physically separated from the second flow path (120, 220) by means of a gas-impermeable heat-conducting barrier (130, 230); • the first flow path (110, 210) containing a first heat-regenerative packing (115, 215) in physical and heat-conducting contact with the barrier (130, 230); and • the second flow path (120, 220) containing a second heat-conductive packing (125, 225) in physical and heat-conducting contact with the barrier (130, 230), method whereby the heat exchanger (100, 200) alternates between: • a first operating stage during which a hot gas flows from the first gas inlet (111, 211) to the first gas outlet (112, 212) along the first gas flow path (110, 210), thereby coming into contact with and heating the first heat-regenerative packing (115, 215), while no gas flows along the second gas flow path (120, 220), and • a second operating stage during which a gas to be heated flows from the second gas inlet (121, 221) to the second gas outlet (122, 222) along the second gas flow path (120, 220), thereby coming into contact with and being heated by the second heat-conductive packing (125, 225) while no gas flows along the first gas flow path (110, 210). • a first gas inlet (111, 211), a first gas outlet (121, 221) and a first gas flow path (110, 210) extending from the first gas inlet (111, 211) to the first gas outlet (112, 212); • a second gas inlet (121, 221), a second gas outlet (122, 222) and a second gas flow path (120, 220) extending from the second gas inlet (121,221) to the second gas outlet (122, 222); the first flow path (110, 210) being in thermal contact with but physically separated from the second flow path (120, 220) by means of a gas-impermeable heat-conducting barrier (130, 230); • the first flow path (110, 210) containing a first heat-regenerative packing (115, 215) in physical and heat-conducting contact with the barrier (130, 230); and • the second flow path (120, 220) containing a second heat-conductive packing (125, 225) in physical and heat-conducting contact with the barrier (130, 230), method whereby the heat exchanger (100, 200) alternates between: • a first operating stage during which a hot gas flows from the first gas inlet (111, 211) to the first gas outlet (112, 212) along the first gas flow path (110, 210), thereby coming into contact with and heating the first heat-regenerative packing (115, 215), while no gas flows along the second gas flow path (120, 220), and • a second operating stage during which a gas to be heated flows from the second gas inlet (121, 221) to the second gas outlet (122, 222) along the second gas flow path (120, 220), thereby coming into contact with and being heated by the second heat-conductive packing (125, 225) while no gas flows along the first gas flow path (110, 210).