Lava channels are abundant on the surface of both the Moon and Venus. There is evidence that erosion may have played a part in their formation. Here a study of the relationship between thermal conductivity and erosion rate is presented. A numerical model is used to investigate the sensitivity of the erosion rate to the relative value of the thermal conductivity of the lava, solid substrate and liquid substrate boundary layer. Results show that the highest rates for thermal erosion are achieved by a high liquid substrate and low solid substrate thermal conductivity, and that the thermal erosion process is most sensitive to the liquid substrate's thermal conductivity.¿ 1997 American Geophysical Union