Abstract The steady close-contact melting phenomenon occurring between a phase change material and an isothermally heated flat surface in relative motion is investigated analytically, with the effects of transverse convection across the liquid film and solid–liquid density difference taken into account. Scale analysis is used to estimate the dependence of system variables on characteristic parameters. Also, an analytical solution to a set of simplified model equations is obtained to quantify the effects. Transverse convection can be characterized by a dimensionless interfacial temperature gradient which asymptotically approaches unity/zero with decreasing/increasing the Stefan number. The convection effect in the liquid film can be neglected approximately for the range of the Stefan number less than 0.1. It is found that the solid descending velocity depends linearly on the liquid-to-solid density ratio, and that the ratios of solid descending velocity, film thickness and friction coefficient to the conduction solution are proportional to 3/4, 1/4 and −1/4 powers of the interfacial temperature gradient, respectively.