Two heat transfer modes are involved in the process of melting around a heated horizontal cylinder: conduction and convection. The magnitude of convection is proportional to the Rayleigh number based on the width of the melted region. The importance of natural convection increases with time. For a short period after the beginning of melting, heat transfer is dominated by conduction. A regular perturbation solution is presented to demonstrate the increasing effect of natural convection on the melting process.