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Investigations of a variety of continental rifts and margins worldwide have revealed that a considerable volume of melt can intrude into the crust during continental breakup1,2,3,4,5,6,7,8, modifying its composition and thermal structure. However, it is unclear whether the cause of voluminous melt production at volcanic rifts is primarily increased mantle temperature or plate thinning1,2,8,9,10,11,12. Also disputed is the extent to which plate stretching or thinning is uniform or varies with depth with the entire continental lithospheric mantle potentially being removed before plate rupture13,14,15,16. Here we show that the extensive magmatism during rifting along the southern Red Sea rift in Afar, a unique region of sub-aerial transition from continental to oceanic rifting, is driven by deep melting of hotter-than-normal asthenosphere. Petrogenetic modelling shows that melts are predominantly generated at depths greater than 80 kilometres, implying the existence of a thick upper thermo-mechanical boundary layer in a rift system approaching the point of plate rupture. Numerical modelling of rift development shows that when breakup occurs at the slow extension rates observed in Afar, the survival of a thick plate is an inevitable consequence of conductive cooling of the lithosphere, even when the underlying asthenosphere is hot. Sustained magmatic activity during rifting in Afar thus requires persistently high mantle temperatures, which would allow melting at high pressure beneath the thick plate. If extensive plate thinning does occur during breakup it must do so abruptly at a late stage, immediately before the formation of the new ocean basin16.