The potential impact of climate change on biodiversity is well documented. A well developed range of statistical methods currently exists that projects the possible future habitat of a species directly from the current climate and a species distribution. However, studies incorporating ecological and evolutionary processes remain limited. Here, we focus on the potential role that local adaptation to climate may play in driving the range dynamics of sessile organisms. Incorporating environmental adaptation into a stochastic simulation yields several new insights. Counter-intuitively, our simulation results suggest that species with broader ranges are not necessarily more robust to climate change. Instead, species with broader ranges can be more susceptible to extinction as locally adapted genotypes are often blocked from range shifting by the presence of cooler adapted genotypes that persist even when their optimum climate has left them behind. Interestingly, our results also suggest that it will not always be the cold-adapted phenotypes that drive polewards range expansion. Instead, range shifts may be driven by phenotypes conferring adaptation to conditions prevalent towards the centre of a species' equilibrium distribution. This may have important consequences for the conservation method termed predictive provenancing. These initial results highlight the potential importance of local adaptation in determining how species will respond to climate change and we argue that this is an area requiring urgent theoretical and empirical attention.