Hydrogen storage within a metal hydride involves exothermic and endothermic processes for hydrogen absorption and desorption, respectively. In addition, the thermal conductivity of the particulate metal hydride (i.e., powder) after repeated absorption processes is extremely low compared to its bulk phase. Low heat conduction through the metal hydride powder makes the hydrogen charging slow; thus, appropriate thermal management is necessary to achieve the fast charging time with the maximum energy density. In this work, we propose a thermal design of a portable hydrogen storage system made of a 300-mL vessel by balancing the internal and external thermal resistances. A copper-mesh structure is employed inside the vessel for enhancing the effective thermal conductivity of metal hydride powder (i.e., reducing the internal thermal resistance). On the other hand, a compact fan is used for enhancing the forced convection heat transfer from the vessel (i.e., reducing the external thermal resistance). Consequently, a copper-mesh structure sacrificing 4.3% of the internal vessel volume was manufactured by following the thermal design. In addition, the effect of the proposed thermal design was confirmed by actual hydrogen-charging experiments that showed 73.5% reduction of the charging time.