Both scaled laboratory experiments and numerical models of terrestrial mantle plumes produce 'balloon-on-a-string' structures, with a bulbous head followed by a stem-like tail. Discussions have focused on whether their initial upwelling heads are hotter than the tails or cooler, as a result of entrainment of ambient mantle during ascent, and also on whether initial plume upwelling is a newtonian or non-newtonian process. The temperature of the mantle delivered to the base of the lithosphere is a critical parameter in such debates. Dry continental magmas can normally contribute little to this topic because their hottest (ultramafic) examples can be expected to be trapped, owing to their density, beneath the Moho. Here we report a rare case in which olivine (with 93.3% forsterite; Mg2SiO4) phenocrysts, precipitated from an unerupted komatiitic melt (approximately 24% MgO) of the Tristan mantle plume head 132 Myr ago, were carried to upper-crust levels in northwest Namibia by less Mg-rich (9.6-18.5% MgO) magmas. We infer that the hidden melt, generated when the plume impinged on the base of the lithosphere, originated in the mantle with a potential temperature of approximately 1,700 degrees C. This is approximately 400 degrees C above ambient and much hotter than the temperatures previously calculated for steady-state Phanerozoic mantle plumes. Published data show that the same conclusion can be reached for the initial Iceland and Galapagos plumes.