Method for producing a filler core with a layered structure, comprising the following steps: - starting from a fiber mat or a nonwoven, made of fibers whose mean fiber diameter is selected as a function of the respectively desired material properties of the filler core to be produced, in particular its insulating and supporting properties, - wherein the fiber mats or nonwovens are inserted into the pressing tool in such a way that a predetermined orientation of the fibers is maintained by a wet forming process or by a dry lay-up after fiber production, so that after completion of the pressing process no fibers of the filler core to be produced extend in the main heat flow direction, - wherein the filler cores are produced within the scope of the method according to the invention in such a way that at first different layers, namely a fiberglass mat (11, 11') each on the upper and lower sides respectively, are inserted into the pressing tool with the interposition of a, preferably light, silicate granulate, preferably at least predominantly consisting of micro hollow glass spheres, - then these fiber mats or nonwovens are compressed by means of a preferably heatable pressing tool to form an at least approximately microporous structure in such a way that a largest possible mean free path length for migrating gas molecules is available within the filler core even if the vacuum is only moderate, wherein the residual gas pressure within the filler core is lowered to a correspondingly lesser extent the more finely porous the structure of the filler core is, in order to deactivate or at least reduce convection via gases, - wherein the degree of compression of the fibers is set depending on the respective fiber diameter in such a way that the filler core has the lowest possible thermal conductivity, wherein there is in this case a respective defined optimum of the degree of compression above and below which the thermal conductivity of the filler core increases, and - wherein a two- or three-dimensional shaping and/or contouring of the filler core takes place by means of the same pressing tool in the same working step, - and the filler core produced by this method is completely free of binders and is held in the predetermined shape solely by mechanical interlocking of the fibers. - starting from a fiber mat or a nonwoven, made of fibers whose mean fiber diameter is selected as a function of the respectively desired material properties of the filler core to be produced, in particular its insulating and supporting properties, - wherein the fiber mats or nonwovens are inserted into the pressing tool in such a way that a predetermined orientation of the fibers is maintained by a wet forming process or by a dry lay-up after fiber production, so that after completion of the pressing process no fibers of the filler core to be produced extend in the main heat flow direction, - wherein the filler cores are produced within the scope of the method according to the invention in such a way that at first different layers, namely a fiberglass mat (11, 11') each on the upper and lower sides respectively, are inserted into the pressing tool with the interposition of a, preferably light, silicate granulate, preferably at least predominantly consisting of micro hollow glass spheres, - then these fiber mats or nonwovens are compressed by means of a preferably heatable pressing tool to form an at least approximately microporous structure in such a way that a largest possible mean free path length for migrating gas molecules is available within the filler core even if the vacuum is only moderate, wherein the residual gas pressure within the filler core is lowered to a correspondingly lesser extent the more finely porous the structure of the filler core is, in order to deactivate or at least reduce convection via gases, - wherein the degree of compression of the fibers is set depending on the respective fiber diameter in such a way that the filler core has the lowest possible thermal conductivity, wherein there is in this case a respective defined optimum of the degree of compression above and below which the thermal conductivity of the filler core increases, and - wherein a two- or three-dimensional shaping and/or contouring of the filler core takes place by means of the same pressing tool in the same working step, - and the filler core produced by this method is completely free of binders and is held in the predetermined shape solely by mechanical interlocking of the fibers.