Over the past ten years we have numerically modelled the properties of the magmatism generated at four of the key areas where the ‘mantle plume–volcanic margin hypothesis’ is expected to be valid: the North Atlantic, South Atlantic, India–Seychelles and Afar. Our model incorporates many of the original assumptions in the classic White and McKenzie model, with pure shear of the lithospheric mantle, passive upwelling and decompressional melting. Our model is however two- rather than one-dimensional, can capture the rift history (extension rate changes and axis jumps) and tracks mantle depletion during melting. In all four of our study areas we require the sub-lithospheric mantle to be 100 – 200°C hotter than ‘normal’, non-volcanic margins to explain the characteristics of the magmatism. In the three passive margin cases we find this excess temperature is limited to a 50 – 100 km thick layer. We require this layer temperature to drop along-strike away from the proposed sites of plume impact at the base of the lithosphere. However, we also find that lithospheric thickness and rift history are as important as temperature for controlling the magmatism. Our work therefore lends support to the hypothesis that the excess magmatism at volcanic margins is due to a thermal anomaly in the asthenosphere, albeit with consideration of extra parameters.