Predicted future climate change will alter species’ distributions as they attempt to track the most suitable ‘climate window’. Climate envelope models indicate the direction of likely range changes but do not incorporate population dynamics, therefore observed responses may differ greatly from these projections. We use simulation modelling to explore the consequences of a period of environmental change for a species structured across an environmental gradient. Results indicate that a species’ range may lag behind its climate envelope and demonstrate that the rate of movement of a range can accelerate during a period of climate change. We conclude that the inclusion of both population dynamics and spatial environmental variability is vital to develop models that can both predict, and be used to manage, the impact of changing climate on species’ biogeography.