Heat exchange system with compensation of dimension change of heat storage material and method for exchanging heat by using the heat exchange system

A heat exchange system with at least one heat exchange chamber with heat exchange chamber boundaries which surround at least one heat exchange chamber interior of the heat exchange chamber is provided. The heat exchange chamber boundaries include at least one first opening for guiding in an inflow of at least one heat transfer fluid into the heat exchange chamber interior and at least one second opening for guiding out 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.