Magnesium hydride is cheap and contains 7.7 wt % hydrogen, making it one of the most attractive hydrogen storage materials, However, thermodynamics dictate that hydrogen desorption from bulk magnesium hydride only takes place at or above 300 degrees C, which is a major impediment for practical application. A few results in the literature, related to disordered materials and very thin layers, indicate that lower desorption temperatures are possible. We systematically investigated the effect of crystal grain size on the thermodynamic stability of magnesium and magnesium hydride, using ab initio Hartree-Fock and density functional theory calculations. Also, the stepwise desorption of hydrogen was followed in detail. As expected, both magnesium and magnesium hydride become less stable with decreasing cluster size, notably for clusters smaller than 20 magnesium atoms. However, magnesium hydride destabilizes more strongly than magnesium. As a result, the hydrogen desorption energy decreases significantly when the crystal grain size becomes smaller than similar to 1.3 nm. For instance, an MgH2 crystallite size of 0.9 nm corresponds to a desorption temperature of only 200 degrees C. This predicted decrease of the hydrogen desorption temperature is an important step toward the application of Mg as a hydrogen storage material.