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Ongoing climate change is shifting species distributions and increasing extinction risks globally. It is generally thought that large population sizes and short generation times of marine phytoplankton may allow them to adapt rapidly to global change, including warming, thus limiting losses of biodiversity and ecosystem function. Here, we show that a marine diatom survives high, previously lethal, temperatures after adapting to above-optimal temperatures under nitrogen (N)-replete conditions. N limitation, however, precludes thermal adaptation, leaving the diatom vulnerable to high temperatures. A trade-off between high-temperature tolerance and increased N requirements may explain why N limitation inhibited adaptation. Because oceanic N limitation is common and likely to intensify in the future, the assumption that phytoplankton will readily adapt to rising temperatures may need to be reevaluated.