Plate apparatus for heat transfer, which comprises at least one rectangular channel, through which a fluid can flow and which has an upper and a lower smooth, in particular planar, straight undeformed broad wall (2, 3) and a left and a right side wall (4, 5), wherein the broad walls are thinner than the side walls, the walls of the at least one rectangular channel are connected undetachably and gastightly to one another and the at least one rectangular channel can be flowed through in its linear extent by a fluid in the direction of flow, wherein the broad walls and the side walls together form a cross section through which a fluid can flow and the inside width of which in relation to the inside height is greater than 20 to less than 1000 and wherein the interior space of the at least one rectangular channel is fitted with at least one single-part or multi-part insert which can be withdrawn, through which a flow can pass, which is in surface-area contact with at least one rectangular channel and the outer geometrical extents of which fill the interior space of the at least one rectangular channel, and wherein at least one single-part or multi-part outsert through which a flow can pass is loosely placed on an outer broad wall, over the entire widthwise and linear extent thereof, in surface-area contact with the at least one rectangular channel and/or housing, and wherein the at least one rectangular channel is surrounded together with the at least one outsert on all sides by a closely fitting housing, wherein the housing comprises front and rear flow plates (10, 11), an upper and a lower broad plate (12, 13) parallel to the broad walls of the at least one rectangular channel and outsert plates (14, 15) with openings, slit-shaped openings are present in the flow plates for receiving rectangular channels and all of the housing plates are undetachably connected to one another, wherein the at least one rectangular channel protrudes into the slit-shaped opening of the flow plates and is likewise connected there, and thereby forms an outwardly sealed housing, which has inside separate flow regions, and wherein furthermore compressive forces occurring are transferred from the flow regions to the housing by way of surface-area contacts, and the fluid flow regions (6, 18) separated in the housing lie one over the other, and the directions of through-flow of inserts and outserts cross one another at an angle of 90 degrees in different planes that are offset in height, and the housing has detachable connection adapters for the flow plates (19, 20) and connection adapters for the outsert plates (21, 22), in order to allow a feed and discharge of fluids, and wherein furthermore the through-flow withdrawable inserts and the placed-on outserts comprise at least two straight structured layers (200, 300), which are not deformed in the plane of the layers and the structure of which is formed by rectangular functional webs and gaps (201, 301), wherein the layers fill the associated through-flow space with their geometrical extents and, as a result, support the inner and outer surfaces of the thin broad walls by way of surface-area contacts of the webs, wherein each structured layer has in its linear extent at least one resilient and/or deformable spring web (202, 302), running parallel to the side wall (4, 5) or the end plate, and the spring web is connected by at least one connecting web (203, 303) to the parallelrunning guiding web (204, 304) in the plane of the layers, and a multiplicity of shorter intermediate webs (205, 305) run from the guiding web and/or the spring web to the opposite parallel spring web, and intermediate webs have as a straight continuation of their extent a spring gap (206, 306) with a deformation path (207, 307) and limit a deformation of the spring web, and in the inflow and outflow zones for the fluids a multiplicity of supporting webs (208, 308) of different lengths protrude into the flow region and the webs have surface-area contact on one side with the broad wall and/or with the broad plate and surface-area contact on one side with neighbouring webs of neighbouring layers in order to direct compressive forces that are present into the surrounding outer housing, wherein connecting, intermediate and supporting webs of layers of the inserts and outserts have an angle of inclination α in relation to the respective main direction of flow of 10 to 70 degrees and in each case one of the two layers of inserts and outserts is turned about its own longitudinal axis of the linear extent by 180 degrees and placed on the other layer, whereby the existing angle of inclination α of the webs alternates, as a result of which webs cross one another and form portions that can be flowed through by a fluid and have little back-mixing.