On planets where most of the heat is transported to the surface by igneous activity (extrusive volcanism or near-surface intrusions), surface heatflow at localities well away from regions of current igneous activity need not be even approximately the conductive heatflow through the entire lithosphere but may instead be dominated by the residual heat leaking out from the last igneous event in that locality. On Io, it is likely that (&kgr;&tgr;)1/2≪ lithosphere thickness (&kgr;=thermal diffusivity, &tgr;=typical time between ''resurfacing events) and the background heatflow may be very large, comparable or even larger than the current observational heatflow, which is associated with the hotspots alone. This upward revision of Io's heatflow is compatible with observations and with recent indications of a non-steady tidal and thermal evolution. On Venus, (&kgr;&tgr;)1/2 is probably comparable to the lithosphere thickness and the resulting upward revision of heatflow may be only marginally significant, unless magmatic activity is enormously greater than on Earth. ¿ American Geophysical Union 1988