An apparatus for transferring heat from a first fluid to a second fluid, which is separated from the first fluid, having a stack-like or saucer-like structure comprising at least two plies (1, 2, 3), in particular plates (1, 2, 3), whereby each ply (1, 2, 3) comprises a heat-transferring area that has numerous passages (11, 12, 13), an inlet area located in front of the heat-transferring area in the direction of flow, and an exit area located behind the heat-transferring area in the direction of flow is proposed in which a relatively large heat-transferring surface area is realized in a small volume, hereby ensuring uninterrupted operation, even when the pressure differential between the two fluids is great. This is achieved according to the invention in that the inlet and/or exit area comprises at least one support element (18).