Rapid evolution in response to environmental change will likely be a driving force determining the distribution of species across the biosphere in coming decades. This is especially true of microorganisms, many of which may evolve in step with warming, including phytoplankton, the diverse photosynthetic microbes forming the foundation of most aquatic food webs. Here we tested the capacity of a globally important, model marine diatom Thalassiosira pseudonana, for rapid evolution in response to temperature. Selection at 16 and 31°C for 350 generations led to significant divergence in several temperature response traits, demonstrating local adaptation and the existence of trade-offs associated with adaptation to different temperatures. In contrast, competitive ability for nitrogen (commonly limiting in marine systems), measured after 450 generations of temperature selection, did not diverge in a systematic way between temperatures. This study shows how rapid thermal adaptation affects key temperature and nutrient traits and, thus, a population's long-term physiological, ecological, and biogeographic response to climate change.