The upward flux of heat from the subsurface core of Warm Deep Water (WDW) to the perennially ice-covered sea surface over the continental slope in the western Weddell Sea is estimated using data obtained during February--June 1992 from a drifting ice station. Through the permanent pycnocline the diapycnal heat flux is estimated to be about 3 W m-2, predominantly because of double-diffusive convection. There is no evidence that shear-driven mixing is important in the pycnocline. The estimated mean rate of heat transfer from the mixed layer to the ice is 1.7 W m-2, although peak heat fluxes of up to 15 W m-2 are found during storms. It is hypothesized that isopycnal mixing along sloping intrusions also contributes to the loss of heat from the WDW in this region; however, we are unable to quantify the fluxes associated with this process. Intrusions occur intermittently throughout this experiment but are most commonly found near the boundary of the warm-core current and the shelf-modified water to the east. These heat fluxes are significantly lower than the basin-averaged value of 19 W m-2 (Fahrbach et al., 1994) that is required to balance the heat budget of the Weddell Gyre. Other studies suggest that shelf processes to the west of the ice station drift track and more energetic double-diffusive convection in the midgyre to the east could account for the difference between our flux estimates for this region and those based on the basin-scale heat budget. ¿ American Geophysical Union 1995