Variations in the phase velocity of fundamental‐mode Rayleigh waves across the Indian Ocean are determined using two inversion approaches. First, variations in phase velocity as a function of seafloor age are estimated using a pure‐path age‐dependent inversion method. Second, a two‐dimensional parameterization is used to solve for phase velocity within 1.25° × 1.25° grid cells. Rayleigh wave travel time delays have been measured between periods of 38 and 200 s. The number of measurements in the study area ranges between 4139 paths at a period of 200 s and 22,272 paths at a period of 40 s. At periods < 100 s, the phase velocity variations are strongly controlled by seafloor age and shown to be consistent with temperature variations predicted by the half‐space‐cooling model for a mantle potential temperature of 1400°C. The inferred thermal structure beneath the Indian Ocean is most similar to the structure of the Pacific upper mantle, where phase velocities can also be explained by a half‐space‐cooling model. The thermal structure is not consistent with that of the Atlantic upper mantle, which is best fit by a plate‐cooling model and requires a thin plate. Removing age‐dependent phase velocity from the 2‐D maps of the Indian Ocean highlights anomalously high velocities at the Rodriguez Triple Junction and the Australian‐Antarctic Discordance and anomalously low velocities immediately to the west of the Central Indian Ridge.