Understanding the enigmatic intraplate volcanism in the Tristan da Cunha region requires knowledge of the temperature of the lithosphere and asthenosphere beneath it. We measured phasevelocity curves of Rayleigh waves using cross-correlation of teleseismic seismograms from an array of ocean-bottom seismometers around Tristan, constrained a region-average, shear-velocity structure, and inferred the temperature of the lithosphere and asthenosphere beneath the hotspot. The ocean-bottom data set presented some challenges, which required data-processing and measurement approaches different from those tuned for land-based arrays of stations. Having derived a robust, phase-velocity curve for the Tristan area, we inverted it for a shear wave velocity profile using a probabilistic (Markov chain Monte Carlo) approach. The model shows a pronounced low-velocity anomaly from 70 to at least 120 km depth. VS in the low velocity zone is 4.1–4.2 km/s, not as low as reported for Hawaii (�4.0 km/s), which probably indicates a less pronounced thermal anomaly and, possibly, less partial melting. Petrological modeling shows that the seismic and bathymetry data are consistent with a moderately hot mantle (mantle potential temperature of 1,410–1,4308C, an excess of about 50–1208C compared to the global average) and a melt fraction smaller than 1%. Both purely seismic inversions and petrological modeling indicate a lithospheric thickness of 65–70 km, consistent with recent estimates from receiver functions. The presence of warmer-than-average asthenosphere beneath Tristan is consistent with a hot upwelling (plume) from the deep mantle. However, the excess temperature we determine is smaller than that reported for some other major hotspots, in particular Hawaii.