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The Eocene (56-34My ago) is one of the best analogs for a greenhouse climate, with high CO2 concentrations, generally high temperatures, and no polar ice caps. A major feature of the Eocene geochemical records suggests a reduced latitudinal gradient, in which most of the warming occurs in polar regions (possibly exceeding 30°C in the Antarctic margin), but less in the tropics. These results could have profound implications for understanding polar amplification of greenhouse warming, but they are not captured in climate models, pointing to important gaps in climate models and to major uncertainties in the geochemical data. We combine two temperature proxies - carbonate clumped isotopes in fossil bivalve shells and archaeal lipid TEX86 in the sediment associated with the bivalves - to constrain Eocene temperatures in Southern high latitudes. Clumped isotope paleothermometry is a thermodynamically controlled temperature proxy that is not dependent on the isotopic composition of seawater, and presents a novel opportunity to reduce uncertainties in Eocene sea surface temperature estimates. We use it to constrain the calibration of TEX86 in order to compare paleotemperatures in the Antarctic Peninsula (Seymour Island) to those in the South Pacific (Eastern Tasman Plateau), both at ~65°S paleo-latitude. The data indicates middle to late Eocene paleotemperatures of 10-17C in Seymour Island and ~7°C higher in the Eastern Tasman Plateau, suggesting a pronounced zonal heterogeneity in southern high latitude sea surface temperatures.