Accurately predicting and mitigating the effects of climate change on species ranges and interactions is a critical challenge. In particular, mosquito-borne diseases like malaria and dengue are poised to shift with climate change. Understanding this impact hinges on a key open question: How will mosquitoes adapt to climate change? Here we adapt a simple framework widely used in conservation biology—evolutionary rescue models—to investigate the potential for mosquito climate adaptation, and we synthesize current evidence, focusing on adaptation to rising temperatures. Short mosquito generation times, high population growth rates, and strong temperature-imposed selection favor mosquito thermal adaptation. However, knowledge gaps about the extent of phenotypic and genotypic variation in thermal tolerance within mosquito populations, the environmental sensitivity of selection, and the role of phenotypic plasticity constrain our ability to make more precise estimates. Future research efforts should prioritize filling these data gaps. Specifically, we outline how common garden and selection experiments can be used to this end. Collecting and incorporating these data into an evolutionary rescue framework will improve estimates of mosquito adaptive potential and of changes in mosquito-borne disease transmission under climate change, and this approach can be applied more broadly to pests as well as species of conservation concern.