If climate change outpaces the rate of adaptive evolution within a site, populations previously well adapted to local conditions may decline or disappear, and banked seeds from those populations will be unsuitable for restoring them. However, if such adaptational lag has occurred, immigrants from historically warmer climates will outperform natives and may provide genetic potential for evolutionary rescue. We tested for lagging adaptation to warming climate using banked seeds of the annual weed Arabidopsis thaliana in common garden experiments in four sites across the species' native European range: Valencia, Spain; Norwich, United Kingdom; Halle, Germany; and Oulu, Finland. Genotypes originating from geographic regions near the planting site had high relative fitness in each site, direct evidence for broad-scale geographic adaptation in this model species. However, genotypes originating in sites historically warmer than the planting site had higher average relative fitness than local genotypes in every site, especially at the northern range limit in Finland. This result suggests that local adaptive optima have shifted rapidly with recent warming across the species' native range. Climatic optima also differed among seasonal germination cohorts within the Norwich site, suggesting that populations occurring where summer germination is common may have greater evolutionary potential to persist under future warming. If adaptational lag has occurred over just a few decades in banked seeds of an annual species, it may be an important consideration for managing longer-lived species, as well as for attempts to conserve threatened populations through ex situ preservation.