Melting heat transfer in open-cell metal foams embedded in phase-change materials (PCMS) predicted by the volume-averaged method (VAM) was systematically compared with that calculated using direct numerical simulation (DNS), with particular attention placed upon the contribution of natural convection in the melt region to overall phase change heat transfer. The two-temperature model based on the assumption of local thermal non equilibrium was employed to account for the large difference of thermal conductivity between metallic ligaments and PCM (paraffin). The Forchheimer extended Darcy model was employed to describe the additional flow resistance induced by metal foam. For the DNS, a geometric model of metal foam based on tetrakaidehedron cells was reconstructed. The DNS results demonstrated significant temperature difference between ligament surface and PCM, thus confirming the feasibility of local thermal non-equilibrium employed in VAM simulations. Relative to the DNS results, the VAM combined with the two-temperature model could satisfactorily predict transient solid-liquid interface evolution and local temperature distribution, although pore-scale features of phase change were lost. The presence of natural convection affected significantly the melting front shape, temperature distribution and full melting. The contribution of natural convection to overall phase change heat transfer should be qualitatively and quantitatively given sufficient consideration from both macroscopic (VAM) and microscopic (DNS) point of views. Besides, practical significance and economic prospective using metal foam in TES unit for WHR system to provide residential heating or hot water is discussed and analyzed.