One of the important tasks of improving the properties of metal hydride reactors is the design of system with optimized heat and mass transfer. Many works are devoted to the selection of the optimal heat exchanger for metal hydride hydrogen storage systems. At the same time, it is necessary to consider the composition of the metal hydride bed, which affects thermal conductivity as well. Little attention has been paid to the study of heat transfer properties in hydrogen storage systems with a heat exchanger and a metal hydride bed based on magnesium hydride and carbon nanotubes. In this work we used numerical simulation to determine the effectiveness of carbon nanotubes addition and heat exchangers with different fin number and geometries on high-temperature magnesium-based hydrogen storage tanks performance. It was found, that increasing the number of fins from three to five makes a smaller contribution in the temperature increasing as compared to the addition of three fins to the heater. The three solid, radial and complex fins have a similar effect on the average Mg/MgH2 bed temperature at 60 min. The most optimal fin number and geometry is three radial fins in terms of the efficiency and the volume it occupies. The addition of carbon nanotubes increases the average temperature of the Mg/MgH2 bed by 67 K for a reactor equipped with a heater without fins. Hydrogen storage system with three radial fins and Mg/MgH2 bed enhanced with carbon nanotubes provides an increase in the average bed temperature of about 180 K as compared to system without fins and nanotubes. This leads to a reduction in the hydrogen absorption time to reach 90% saturation by almost 63% for the three radial fins reactor with carbon nanotubes addition to the metal hydride bed. It has been confirmed that the addition of carbon nanotubes to Mg/MgH2 makes a significant contribution to the heat transfer in the metal hydride bed. In addition, it is shown that both an increase in the heat transfer area and the thermal conductivity coefficient leads to a significant improvement in the efficiency of the metal hydride reactor. In the future, the obtained results can be taken into account when designing hydrogen storage systems based on these materials.