Most range shift predictions focus on the dispersal phase of the colonization process. Because moving populations experience increasingly dissimilar nonclimatic environmental conditions as they track climate warming, it is also critical to test how individuals originating from contrasting thermal environments can establish in nonlocal sites. We assess the intraspecific variation in growth responses to nonlocal soils by planting a widespread grass of deciduous forests (Milium effusum) into an experimental common garden using combinations of seeds and soil sampled in 22 sites across its distributional range, and reflecting movement scenarios of up to 1600 km. Furthermore, to determine temperature and forest-structural effects, the plants and soils were experimentally warmed and shaded. We found significantly positive effects of the difference between the temperature of the sites of seed and soil collection on growth and seedling emergence rates. Migrant plants might thus encounter increasingly favourable soil conditions while tracking the isotherms towards currently 'colder' soils. These effects persisted under experimental warming. Rising temperatures and light availability generally enhanced plant performance. Our results suggest that abiotic and biotic soil characteristics can shape climate change-driven plant movements by affecting growth of nonlocal migrants, a mechanism which should be integrated into predictions of future range shifts.