This note draws attention to a result of conduction theory which appears to be little known but is relevant to the development of approximate integral models of flame spread. A semi-infinite plane, emitting a flux of heatq″per unit area whilst travelling at velocityUparallel to the surface of a sink to which the heat source is perpendicular, transfers heat to the sink at a rate (2/π)q″k/Uper unit width wherekis the thermal diffusivity of the medium. This result is compared to the result of a more complex flame spread theory.