Temperature differences between lavas erupted at ocean islands and mid-ocean ridges are crucial to documenting the existence of mantle plumes. Olivines are useful for T estimation because they provide a less homogenized account of the melting process compared to glass and whole rock samples. Olivine-liquid equilibria, and olivine phenocrysts from Hawaii, Iceland, and several mid-ocean ridge localities, indicate higher melting temperatures compared to mid-ocean ridges (MORs) by at least ~250 ¿ 52¿C and 165 ¿ 62¿C, respectively. When translated to differences in mantle potential temperature, ΔTp, Hawaii and Iceland potential temperatures are hotter than ambient MORs by 213--235 and 162--184¿C, respectively, similar to estimates required by geodynamic models for mantle thermal upwellings. Absolute mantle potential temperatures are more uncertain as they depend on estimates of melt fraction and depth of equilibration, but olivine-liquid equilibria support the following estimates: TpHawaii = 1688¿C; TpIceland = 1637¿C; TpMORs = 1453--1475¿C. All of these estimates include the effects of H2O, Na2O + K2O, and SiO2 on olivine-melt equilibria and are robust against other variations in source or liquid composition, such as FeO and CO2. These estimates show that at least at Iceland and Hawaii, volcanism is driven by large temperature anomalies whose magnitudes are consistent with the existence of thermally driven mantle plumes.