This paper reports a theoretical and experimental study of the effect of solid-side subcooling on the phenomenon of melting by natural convection at the vertical interface between a solid body and a pool of its own liquid. The first part of the study consists of a conjugate boundary layer analysis of the transient melting process, in which the effect of solid subcooling leads to the formation of a time-dependent conduction boundary layer in the solid. The theoretical solution documents not only the effect of solid subcooling on the melting rate, but also the effects of liquid superheating (Stefan number) and thermal diffusivity ratio. The second part of the study consists of melting experiments conducted in a rectangular enclosure heated at a constant rate from the side. The solid subcooling parameter B covers the range 0.3–6.3, as the Rayleigh number remains fixed. The experiments show that in the conduction-dominated regime the Nusselt number increases as B increases. In the convection-dominated regime, the effect of the subcooling parameter B is insignificant. It is shown that these experimental observations agree with the trends anticipated theoretically in the first part of the study.