In a regenerative heat exchanger of the kind having a rotor (2) mounted in a casing (1), supports (10) are provided for maintaining a certain clearance between the rotor (2) and movable plates (6, 8) connected to the casing (1) and located closed to the rotor ends. Each support co-operates through a guided surface (62) on a sliding shoe (25) with a guiding surface (61) on a flange (12) on the rotor (2). According to the invention the support (10) is provided with water conduit means (63, 65, 66) ending in the guided surface (62) and being connected to a water source of a pressure sufficient to establish a gap between the guided (62) and the guiding (61) surface so that a cushion of vaporized water is established between the surfaces (61, 62) as the water vaporizes by contact with the guiding surface (61), which is hot, and escapes from the conduit means (63, 65, 66) through the gap.