The pattern of heat flow from the Barbados Ridge accretionary complex has been derived from marine surveys with heat flow probes, from measurements in drill holes, and from the depths of bottom-simulating seismic reflectors caused by gas hydrate. The heat flow from the accretionary complex has been simulated using a finite-difference model to investigate how heat flow responds to changes in the cross-sectional shape of the complex and the rate of convergence, and to variations in pore-fluid pressure within the complex and along the decollement at its base. In the south of the complex, heat flow decreases westward from the toe of the wedge, towards the island arc, because the downward movement of subducting lithosphere beneath the wedge and the active thickening of the accreted sedimentary sequence reduce the geothermal gradient more rapidly than thermal diffusion can maintain it. Localized high anomalies, attributed to the flow of warm fluids along fault zones, are superimposed on the conductive heat flow patterns. Farther west, heat flow increases arcward, produced partly by thermal diffusion re-establishing a steeper thermal gradient where the rate of thickening is decreased, but mainly by the arcward increase of frictional heating along the base of the wedge caused by the increase of slip rate and increased normal stress arising from thickening of the wedge. In the north of the complex, around the ODP Leg 110 drill sites, the conductive model cannot reproduce the anomalously high heat flow measurements, which can only be explained by the advection of warm pore fluids. ¿ American Geophysical Union 1993