Thermal energy storage has the potential to decarbonize the heating sector, facilitating the use of renewable energy sources, in particular solar thermal energy. In this paper we present a study on thermochemical storage material composed of inorganic salts hosted in the porous matrix of zeolite 13X; we prepared a series of composites containing different amounts of inorganic salts - MgCl2, MgSO4 by impregnation method and we characterized them by multiple experimental techniques: energy storage and adsorption/desorption rates were assessed using simultaneous thermal analysis by coupling thermogravimetric and differential scanning calorimetry, microstructure, and composition were assessed through scanning electron microscopy and energy-dispersive X-ray spectroscopy. Finally, thermal conductivity was measured by laser flash analysis. With our composite material, we achieved an energy density of 400 kJ/kg across the temperature range 30-150 degrees C and a 35% increase in thermal conductivity by adding 1% of multiwall carbon nanotubes. These features make the material an interesting option for thermal storage in buildings. We attribute the behavior of the material to the combination of large zeolite-specific area coupled with the heat of water sorption/hydration of MgCl2, MgSO4.