This paper presents a numerical analysis of natural convection-dominated melting from a wall of finite conductance. A computational methodology based on a stream function / vorticity / temperature formulation is presented. The irregular shape of the moving solid-liquid phase front is treated with generalized curvilinear coordinates. The model is then employed to investigate the interaction between convection in the cavity filled with phase change material (PCM) and conduction in the heated wall. Experiments are carried out for Rayleigh numbers between 2.03 × 105and 4.60 × 109, wall-PCM thermal diffusivity ratios α between 1.0 and 1000.0, and dimensionless wall thicknesses w between 0.005 and 0.25. The results indicate that for α < 10 and increasing wall thickness, conduction plays a significant role in the melting process. It delays the onset of buoyancy-driven convection and, as a result, slows down melting. In return, buoyancy-driven motion of the melt influences conduction heat transfer across the wall.