Climate change affects marine organisms, causing migrations, biomass reduction and extinctions1,2. However, the abilities of marine species to adapt to these changes remain poorly constrained on both geological and anthropogenic timescales. Here we combine the fossil record and a global trait-based plankton model to study optimal temperatures of marine calcifying zooplankton (foraminifera, Rhizaria) through time. The results show that spinose foraminifera with algal symbionts acclimatized to deglacial warming at the end of the Last Glacial Maximum (LGM, 19–21 thousand years ago, ka), whereas foraminifera without symbionts (non-spinose or spinose) kept the same thermal preference and migrated polewards. However, when forcing the trait-based plankton model with rapid transient warming over the coming century (1.5 °C, 2 °C, 3 °C and 4 °C relative to pre-industrial baseline), the model suggests that the acclimatization capacities of all ecogroups are limited and insufficient to track warming rates. Therefore, foraminifera are projected to migrate polewards and reduce their global carbon biomass by 5.7–15.1% (depending on the warming) by 2100 relative to 1900–1950. Our study highlights the different challenges posed by anthropogenic and geological warming for marine plankton and their ecosystem functions. Data from the fossil record, together with computational modelling, are used to assess the response of foraminifera (marine zooplankton) to temperature changes through time and to predict how well they will adjust to future climate-change-induced ocean warming.