Heat exchange system, with - at least two heat exchange chambers (11, 12), - each of the heat exchange chambers (11, 12) comprises heat exchange chamber boundaries which surround at least one heat exchange chamber interior of the heat exchange chamber (11, 12), wherein - the heat exchange chamber boundaries comprise at least one first opening for guiding in of an inflow of at least one heat transfer fluid into the heat exchange chamber interior and at least one second opening for guiding out of an outflow of the heat transfer fluid out of the heat exchange chamber interior; - at least one heat storage material is arranged in the heat exchange chamber interior such that a heat exchange flow of the heat transfer fluid through the heat exchange chamber interior causes a heat exchange between the heat storage material and the heat transfer fluid; - the heat exchange flow through the heat exchange chamber interior of the each of the heat exchange chambers (11, 12) can be adjusted individually with the aid of at least one flow adjusting element; characterised in that - the heat exchange chambers (11, 12) are horizontal heat exchange chambers; - the heat exchange chamber interiors of the heat exchange chambers (11, 12) are serially connected together such that the inflow of the heat transfer fluid into the heat exchange chamber interior of one of the heat exchange chambers (11, 12) comprises the outflow of the heat transfer fluid out of the heat exchange chamber interior of the other heat exchange chamber (12, 11); and - the heat exchange chambers (11, 12) are individually activatable or deactivatable. - at least two heat exchange chambers (11, 12), - each of the heat exchange chambers (11, 12) comprises heat exchange chamber boundaries which surround at least one heat exchange chamber interior of the heat exchange chamber (11, 12), wherein - the heat exchange chamber boundaries comprise at least one first opening for guiding in of an inflow of at least one heat transfer fluid into the heat exchange chamber interior and at least one second opening for guiding out of an outflow of the heat transfer fluid out of the heat exchange chamber interior; - at least one heat storage material is arranged in the heat exchange chamber interior such that a heat exchange flow of the heat transfer fluid through the heat exchange chamber interior causes a heat exchange between the heat storage material and the heat transfer fluid; - the heat exchange flow through the heat exchange chamber interior of the each of the heat exchange chambers (11, 12) can be adjusted individually with the aid of at least one flow adjusting element; characterised in that - the heat exchange chambers (11, 12) are horizontal heat exchange chambers; - the heat exchange chamber interiors of the heat exchange chambers (11, 12) are serially connected together such that the inflow of the heat transfer fluid into the heat exchange chamber interior of one of the heat exchange chambers (11, 12) comprises the outflow of the heat transfer fluid out of the heat exchange chamber interior of the other heat exchange chamber (12, 11); and - the heat exchange chambers (11, 12) are individually activatable or deactivatable.