This invention provides for an apparatus and a method for operation of a cryogenic hydrogen storage system that contains a porous medium configured to adsorb hydrogen. The hydrogen storage and supply system includes a hydrogen source apparatus and a cryosorptive storage apparatus. Methods and devices that allow for an energy efficient filling of the cryosorptive apparatus from the hydrogen source apparatus are described. The cryosorptive hydrogen storage apparatus is filled with cold, pressurized hydrogen. During the course of filling, heat is generated in the cryosorptive storage device by the process of hydrogen adsorption on to the host medium. Methods and devices are provided for the removal the generated heat and the warm hydrogen. Further provided are devices and methods for the capture and recycle of escaped hydrogen within the hydrogen source apparatus.