The role of self-intercalation in 2D van der Waals materials is key to the understanding of many of their properties. Here we show that the magnetic ordering temperature of thin films of the 2D ferromagnet Fe_{5}GeTe_{2} is substantially increased by self-intercalated Fe that resides in the van der Waals gaps. The epitaxial films were prepared by molecular beam epitaxy and their magnetic properties explored by element-specific x-ray magnetic circular dichroism that showed ferromagnetic ordering up to 375 K. Both surface and bulk sensitive x-ray absorption modes were used to confirm that the magnetic signal is of an intrinsic nature. Fe occupation within the van der Waals gap was determined by x-ray diffraction which showed a notably higher occupation with respect to bulk crystals. We thus infer, supported by first-principles calculations, that the higher magnetic ordering temperature results from an increased exchange interaction between the individual Fe_{5}GeTe_{2} layers mediated by Fe atoms residing within the van der Waals gaps. Our findings establish self-intercalation during epitaxial growth as an efficient mechanism to achieve high-temperature magnetism in a broad class of van der Waals materials.