The invention relates to a magnetocaloric lattice element formed by fibres of magnetocaloric material, wherein the fibres are arranged in respective parallel lattice planes, each fibre having a respective mass of magnetocaloric material, the fibres of a given lattice plane do not contact each other but each fibre of a given lattice plane is attached to at least two fibres in a next neighbouring lattice plane, and wherein the magnetocaloric lattice element exhibits exactly one predominant mass-weighted direction of longitudinal fibre extension. When arranged in alignment of its predominant mass-weighted direction of longitudinal fibre extension with an external magnetic field, the magnetocaloric lattice element achieves an advantageous, particularly high magnetization of the magnetocaloric material, and as a consequence improves the performance of the magnetocaloric cooling device.