Earth's climate cooled from a period of extreme warmth in the early Eocene Epoch (ca. 50 Ma) to the early Oligocene (ca. 33 Ma), when a large ice cap first appeared on Antarctica. Evidence from the planktonic foraminifer oxygen isotope record in deep-sea cores has suggested that tropical sea-surface temperatures declined by 5-10 degrees over this interval, eventually becoming much cooler than modern temperatures. Here we present paleotemperature estimates from foraminifer isotopes and the membrane lipids of marine Crenarcheota from new drill cores in Tanzania that indicate a warm and generally stable tropical climate over this period. We reinterpret the previously published isotope records in the light of comparative textural analysis of the deep-sea foraminifer shells, which shows that in contrast to the Tanzanian material, they have been diagenetically recrystallized. We suggest that increasingly severe alteration of the deep-sea plankton shells through the Eocene produced a diagenetic overprint on their oxygen isotope ratios that imparts the false appearance of a tropical sea-surface cooling trend. This implies that the long-term Eocene climatic cooling trend occurred mainly at the poles and had little effect at lower latitudes.