<p>Whether movement will enable organisms to alleviate thermal stress is central to the biodiversity implications of climate change. We use the temperature-dependence of ectotherm performance to investigate the fitness consequences of movement. Movement to an optimal location within a 50 km radius will only offset the fitness impacts of climate change by 2100 in 5 per cent of locations globally. Random movement carries an 87 per cent risk of further fitness detriment. Mountainous regions with high temperature seasonality (i.e. temperate areas) not only offer the greatest benefit from optimal movement but also the most severe fitness consequences if an organism moves to the wrong location. Doubling dispersal capacity would provide modest benefit exclusively to directed dispersers in topographically diverse areas. The benefits of movement for escaping climate change are particularly limited in the tropics, where fitness impacts will be most severe. The potential of movement to lessen climate change impacts may have been overestimated.</p>