We examine how the steady free convective boundary-layer flow induced by a vertical heated surface is affected by the presence of sinusoidal surface temperature variations about a constant mean value which is above the ambient fluid temperature. The problem is studied using fully numerical techniques and an asymptotic analysis which is valid at large distances from the leading edge. The surface rate of heat transfer eventually alternates in sign with distance from the leading edge, but no separation occurs unless the amplitude of the thermal modulation is sufficiently high. The agreement between the numerical results and a two-term asymptotic analysis is excellent.