Based on the sensitivity of species to ongoing climate change, and numerous challenges they face tracking suitable conditions, there is growing interest in species' capacity to adapt to climatic stress. Here, we develop and apply a new generic modelling approach (AdaptR) that incorporates adaptive capacity through physiological limits, phenotypic plasticity, evolutionary adaptation and dispersal into a species distribution modelling framework. Using AdaptR to predict change in the distribution of 17 species of Australian fruit flies (Drosophilidae), we show that accounting for adaptive capacity reduces projected range losses by up to 33% by 2105. We identify where local adaptation is likely to occur and apply sensitivity analyses to identify the critical factors of interest when parameters are uncertain. Our study suggests some species could be less vulnerable than previously thought, and indicates that spatiotemporal adaptive models could help improve management interventions that support increased species' resilience to climate change.