Rifted margins form from extension and breakup of the continental lithosphere. If this extension is coeval with a region of hotter lithosphere, then it is generally assumed that a volcanic margin would follow. Here we present the results of numerical simulations of rift margin evolution by extending continental lithosphere above a thermal anomaly. We find that unless the lithosphere is thinned prior to the arrival of the thermal anomaly or half spreading rates are more than ̃50 mm a^-1, the lithosphere acts as a lid to the hot material. The thermal anomaly cools significantly by conduction before having an effect on decompression melt production. If the lithosphere is thinned by the formation of extensional basins then the thermal anomaly advects into the thinned region and leads to enhanced decompression melting. In the North Atlantic a series of extensional basins off the coast of northwest Europe and Greenland provide the required thinning. This observation suggests that volcanic margins that show slow rates of extension only occur where there is the combination of a thermal anomaly and previous regional thinning of the lithosphere.