We image the lithospheric and upper asthenospheric structure of western continental Yemen with 24 broadband stations to evaluate the role of the Afar plume on the evolution of the continental margin and its extent eastwards along the Gulf of Aden. We use teleseismic tomography to compute relative P-wave velocity variations in southwestern Yemen down to 300 km depth. Published receiver function analysis suggest a dramatic and localized thinning of the crust in the vicinity of the Red Sea and the Gulf of Aden, consistent with the velocity structure that we retrieve in our model. The mantle part of the model is dominated by the presence of a low velocity anomaly in which we infer partial melting just below thick Oligocene flood basalts and recent off-axis volcanic events (from 15 Ma to present). This low velocity anomaly could correspond to an abnormally hot mantle and could be responsible for dynamic topography and recent magmatism in western Yemen. Our new P-wave velocity model beneath western Yemen suggests the young rift flank volcanoes beneath margins and on the flanks of the Red Sea rift are caused by focused small-scale diapiric upwelling from a broad region of hot mantle beneath the area. Our work shows that relatively hot mantle, along with partial melting of the mantle, can persist beneath rifted margins after breakup has occurred.