We report 70 measurements of conductive heat flow at the 50-m-high, 200-m-diameter TAG active hydrothermal mound, made during submersible surveys with Alvin in 1993 and 1995 and Shinkai 6500 in 1994. The stations were all measured with 5-thermistor, 0.6- or 1-m-long Alvin heat flow probes, which are capable of determining both gradient and thermal conductivity, and were transponder-navigated to an estimated accuracy of ¿5--10 m relative to the 10-m-diameter central complex of black smokers. Within 20 m of this complex, conductive heat flow values are extremely variable (0.1->100 W/m2), which can only be due to local spatial and possible temporal variability in the immediate vicinity of the vigorous discharge sites. A similar local variability is suggested in the ''Kremlin'' area of white smokers to the southeast of the black smoker complex. On the south and southeast side of the mound, there is very high heat flow (3.7->25 W/m2) on the sedimented terraces that slope down from the Kremlin area. Heat flow is also high (0.3-3 W/m2) in the pelagic carbonate sediments on the surrounding seafloor within a few tens of meters of the southwest, northwest, and northeast sides of the mound. On the west side of the sulfide rubble plateau that surrounds the central black smoker peak, there is a coherent belt of very low heat flow (<20 mW/m2) 20--50 m west of the smokers, suggestive of local, shallow recharge of bottom water. The three submersible surveys spanned nearly two years, but showed no indication of any temporal variability in conductive heat flow over this time scale, whether natural or induced by ODP drilling in 1994. ¿ American Geophysical Union 1996