Volcanic rifted margins show a temporal evolution in igneous crustal thickness and thus provide additional insights into mantle dynamics compared to the steady state situation at mid-ocean ridges. Although details between different provinces vary, volcanic rifted margins generally show a short-lived pulse of extreme magmatism that quickly abates to a steady state mid-ocean ridge. The generation of thick igneous crust at volcanic rifted margins requires either melting of hot mantle material to higher degrees than observed at mid-ocean ridges or melting of larger amounts of mantle material than would be the case for plate-driven upwelling. To assess under what conditions buoyantly driven upwelling or small-scale convection at rifting plate boundaries is important, a fluid dynamical model with non-Newtonian viscosity that includes the feedback from melting on the physical properties of the mantle is developed. To generate a pulse of high magmatic production requires a viscosity and density structure that also leads to excessive fluctuations in magmatic productivity or a sustained high productivity that continues long after breakup. A viscosity increase due to dehydration caused by melting effectively suppresses buoyant upwelling above the depth to the dry solidus, thereby restricting shallow flow to plate-driven upwelling. While this stabilizes the time dependence and forces the productivity to values consistent with mid-ocean ridge accretion, it does so at the expense of eliminating the breakup instability. Models that assume an abrupt change in prerift lithospheric thickness suffer from the same deficits. However, including a sublithospheric hot layer leads to a model that can predict the temporal evolution of igneous crustal thickness observed in refraction seismic data from the southeast Greenland volcanic rifted margin.