As climate change unravels, ecosystems are facing a warming of the climate and an increase in extreme heat events that are unprecedented in recent geological history. We know very little of the ability of oceanic phytoplankton communities, key players in the regulation of Earth's climate by the oceans, to adapt to these changes. Quantifying the resilience of phytoplankton communities to environmental stressors by means of adaptive evolution is however crucial to accurately predict the response of marine ecosystems to climate change. In this work, we use an eco-evolutionary model to simulate the adaptive response of marine phytoplankton to temperature changes in an initially temperate oligotrophic water-column. By exploring a wide range of scenarios of phytoplankton adaptive capacity, we find that phytoplankton can adapt to temperature increases-even very large ones-as long as they occur over the time scale of a century. However, when rapid and extreme events of temperature change are considered, the phytoplankton adaptive capacity breaks down in a number of our scenarios in which primary productivity plummets as a result. This suggests that current Earth System Models implicitly assuming perfect and instantaneous phytoplankton adaptation to temperature might be overestimating the phytoplankton's resilience to climate change.