A methematical model is presented for the cooling of an active flow with two separate thermal components. One component is a crust that cools by radiation and generally thickens with time. The other component is an inner core that is vertically isothermal and partially exposed at the top surface, where heat is lost by radiation. This model provides a more realistic description of active lava flows than the existing models that assume thermal homogeneity in each vertical cross section perpendicular to the direction of flow advance. Characteristic time scales for heat loss from the core are comparable to typical durations for the emplacement of single-lobed basaltic flows. The two-component model predicts fractional areas of exposed core between 0.001 and 0.1, consistent with several types of observations of lava flows. Predicted temperature changes for the crust and core, as a function of distance from the vent, also comparable favorably to the limited observations available for active flows. Depending on eruption duration, fraction of exposed core, flow thickness, and initial eruption temperature, the thermal interaction between the crust and the core can have a significant effect on the core temperature, the growth of the crust, and various averages of thermal losses by radiation. The analysis suggests that flow dimensions may be strongly influenced by thermal dynamics in the core if emplacement duration is long, the fraction of exposed core is maintained at a high level, or the initial eruption temperature is low. ¿ American Geophysical Union 1990