A numerical study on the melting process inside an isothermal spherical capsule is made. It is assumed that the phase change medium of its solid phase is heavier than the liquid phase and therefore the unmelted solid core is continuously moving downward on account of gravity forces. Such a gravity-assisted melting is commonly characterized by the existence of a thin liquid film below the solid core. The present study is motivated to present a full-equation-based analysis of the influences of the initial subcooling and the natural convection on the fluid flow and heat transfer characteristics associated with the gravity-assisted melting. In the light of the solution strategy, the present study is substantially distinguished from the existing works in that the complete set of governing equations in both the melted and unmelted regions are resolved without subdivision of the solution domains. For example, the liquid film region and the upper melted region are treated here as one domain and thus obviating laborious efforts to couple them. Numerical results are obtained by varying the Rayleigh numbers and the degree of subcooling. For the range of parameters examined, the presence of subcooling was found to impede the melting rate. The dropping velocity of the unmelted solid core was observed to affect the natural convection in the liquid significantly. When compared with the available experimental data, much improved prediction was achieved.