Method of operating a hydrogen generator

A hydrogen generator includes: a reformer (102) configured to generate a hydrogen-containing gas by a reforming reaction using a raw material; a combustor (104) configured to heat the reformer; an air supplying device (106) configured to supply combustion air to the combustor; a first heat exchanger (108) configured to recover heat from a flue gas discharged from the combustor; a first heat medium passage (110) through which a first heat medium flows, the first heat medium receiving the heat recovered from the flue gas in the first heat exchanger; a first pump (112) configured to cause the first heat medium in the first heat medium passage to flow; a heat accumulator (140) configured to store the heat recovered by the first heat medium; and a controller (114) configured to cause the first pump to operate in a cooling step that is a step of cooling down at least the reformer by supplying the air from the air supplying device to the combustor in a state where the combustor is not carrying out combustion during a stop processing