The physisorption of molecular hydrogen in model carbon foams has been investigated from 50K to room temperature. The study is carried out within the framework of the density functional theory for quantum liquids at finite temperatures. Calculations are performed in the grand canonical ensemble, i.e., the adsorbed fluid is assumed to be in equilibrium with an external gas of hydrogen molecules with concentrations ranging from 8 × 10 -4 kgm -3 to n=71kgm -3. It is shown that, while strong zero-point energy effects are present even at room temperature, the adsorption isotherms exhibit only a weak dependence on the explicit incorporation of the bosonic exchange symmetry of hydrogen molecules. The increase of the average particle density prevents the deviations from the Maxwell-Boltzmann statistics to become noticeable if the system is cooled down. The volumetric storage capacity of these materials at low temperatures is about one half of the U. S. Department of Energy goal, while the gravimetric capacity is still far from the standards required by mobile applications. The relation between the microscopic structure of the hydrogen fluid and the calculated adsorption properties is also addressed.