Downhole thermal measurements for the southwest Rockall Bank rifted margin made on Deep SeaDrilling Project leg 81, plus those previously made on leg 48, give six reliable heat flow values in the narrow range 62-71 mW m -2, with an average of 66.5 mW m -2. The temperatures were obtained using a self-contained downhole temperature-recording device. A long probe is inserted through the drill bit into the undisturbed sediments below the bottom of the hole at intervals during drilling. The thermal disturbance from the penetration was extrapolated to equilibrium in situ temperatures using the cylindrical decay function. The thermal conductivities have been measured on core samples using the needle probe method supplemented with porosity-conductivity relations. Heat production in the sedimentaryvolcanic sequence above basement probably makes a negligible contribution to the heat flow. There is no systematic heat flow trend with water depth, which ranges from 1650 to 1900 m, or with position, and the mean value is not significantly different from that expected from pure oceanic crust of age equal to the approximately 50-Ma time of rifting. However, the unloaded basement depth is over 1 km shallower than expected for normal oceanic crust of the 50-Ma rifting age. The heat flow combined with subsidence data fits a simple rifting model with crustal stretching and thinning by a factor of 3 or 4 over a zone at least 100 km wide, occurring about 50 Ma. The heat production in the stretched crust is taken to contribute 4 mW m-2, based on a prerift structure comparable to once adjacent North America. A major uncertainty in thermal and subsidence models for the margin is the effect of the earlier "Iceland hot spot" which produced extensive margin volcanism on the northern British Isles and Greenland and shoaling of the oceanic crust at about the time of west Rockall rifting.