As Earth is currently experiencing dramatic climate change, it is of critical interest to understand how species will respond to it. The chance of a species withstanding climate change is likely to depend on the diversity within the species and, particularly, whether there are sub-populations that are already adapted to extreme environments. However, most predictive studies ignore that species comprise genetically diverse individuals. We have identified genetic variants in Arabidopsis thaliana that are associated with survival of an extreme drought event-a major consequence of global warming. Subsequently, we determined how these variants are distributed across the native range of the species. Genetic alleles conferring higher drought survival showed signatures of polygenic adaptation and were more frequently found in Mediterranean and Scandinavian regions. Using geo-environmental models, we predicted that Central European, but not Mediterranean, populations might lag behind in adaptation by the end of the twenty-first century. Further analyses showed that a population decline could nevertheless be compensated by natural selection acting efficiently over standing variation or by migration of adapted individuals from populations at the margins of the species' distribution. These findings highlight the importance of within-species genetic heterogeneity in facilitating an evolutionary response to a changing climate.