A household appliance has a working chamber and at least one latent heat store having a respective storage medium. The storage medium is thermally coupled via a respective associated heat exchanger to a working medium circulating through the working chamber. The working medium moves from the working chamber to a heat sink, from the heat sink to the heat exchanger, from the heat exchanger to a heat source, and from the heat source back to the working chamber. The storage medium forms a substance mixture together with a respective carrier fluid. The substance mixture can be conducted in a respective closed circuit through the associated heat exchanger for an exchange of heat with the working medium, and the substance mixture circulates between the associated heat exchanger and at least one reservoir in the respective closed circuit. The reservoir can be refilled layer-by-layer with the substance mixture conducted through the respective associated heat exchanger.