Current carbon dioxide emissions are an assumed threat to oceanic calcifying plankton (coccolithophores) not just due to rising sea-surface temperatures, but also because of ocean acidification (OA). This assessment is based on single species culture experiments that are now revealing complex, synergistic, and adaptive responses to such environmental change. Despite this complexity, there is still a widespread perception that coccolithophore calcification will be inhibited by OA. These plankton have an excellent fossil record, and so we can test for the impact of OA during geological carbon cycle events, providing the added advantages of exploring entire communities across real-world major climate perturbation and recovery. Here we target fossil coccolithophore groups (holococcoliths and braarudosphaerids) expected to exhibit greatest sensitivity to acidification because of their reliance on extracellular calcification. Across the Paleocene-Eocene Thermal Maximum (56 Ma) rapid warming event, the biogeography and abundance of these extracellular calcifiers shifted dramatically, disappearing entirely from low latitudes to become limited to cooler, lower saturation-state areas. By comparing these range shift data with the environmental parameters from an Earth system model, we show that the principal control on these range retractions was temperature, with survival maintained in high-latitude refugia, despite more adverse ocean chemistry conditions. Deleterious effects of OA were only evidenced when twinned with elevated temperatures.