The Eocene/Oligocene boundary, at about 33.7 Myr ago, marks one of the largest extinctions of marine invertebrates in the Cenozoic period. For example, turnover of mollusc species in the US Gulf coastal plain was over 90% at this time. A temperature change across this boundary--from warm Eocene climates to cooler conditions in the Oligocene--has been suggested as a cause of this extinction event, but climate reconstructions have not provided support for this hypothesis. Here we report stable oxygen isotope measurements of aragonite in fish otoliths--ear stones--collected across the Eocene/Oligocene boundary. Palaeo-temperatures reconstructed from mean otolith oxygen isotope values show little change through this interval, in agreement with previous studies. From incremental microsampling of otoliths, however, we can resolve the seasonal variation in temperature, recorded as the otoliths continue to accrete new material over the life of the fish. These seasonal data suggest that winters became about 4 degrees C colder across the Eocene/Oligocene boundary. We suggest that temperature variability, rather than change in mean annual temperature, helped to cause faunal turnover during this transition.