Climate warming over the next century is expected to have a large impact on the interactions between pathogens and their animal and human hosts. Vector-borne diseases are particularly sensitive to warming because temperature changes can alter vector development rates, shift their geographical distribution and alter transmission dynamics. For this reason, African trypanosomiasis (sleeping sickness), a vector-borne disease of humans and animals, was recently identified as one of the 12 infectious diseases likely to spread owing to climate change. We combine a variety of direct effects of temperature on vector ecology, vector biology and vector-parasite interactions via a disease transmission model and extrapolate the potential compounding effects of projected warming on the epidemiology of African trypanosomiasis. The model predicts that epidemics can occur when mean temperatures are between 20.7 degrees C and 26.1 degrees C. Our model does not predict a large-range expansion, but rather a large shift of up to 60 per cent in the geographical extent of the range. The model also predicts that 46-77 million additional people may be at risk of exposure by 2090. Future research could expand our analysis to include other environmental factors that influence tsetse populations and disease transmission such as humidity, as well as changes to human, livestock and wildlife distributions. The modelling approach presented here provides a framework for using the climate-sensitive aspects of vector and pathogen biology to predict changes in disease prevalence and risk owing to climate change.