Buoyancy-assisted melting of an unconstrained ice in an isothermally heated horizontal enclosure was numerically analyzed in a range of wall temperatures encompassing the density inversion point. The problem as posed here involves two physically distinct domains each of which has its own scales and respective heat transfer mode. These two domains join at the junction where the liquid squeezed out of the film region flushes into the lower melt pool. Both of these domains have been treated separately in the literature by a patching technique which invokes several, otherwise unnecessary, assumptions. The present study eliminates successfully such a superfluous procedure by treating the film and lower melt pool regions as a single domain. As a result of this efficient solution procedure, the interaction of the water stream ejected at the junction and the natural convection in the melt pool could be clarified for different wall temperatures. Though limited by two-dimensionality, the present results conformed indirectly the earlier reported transition of the flow pattern, as the wall temperature was increased over the density inversion point. The transient evolution of the melting surface, the time rate of change in melt volume fraction, the local and temporal variation of the heat transfer coefficients are analyzed and presented.