The latest climate models project widely varying magnitudes of future extreme precipitation changes, thus impeding effective adaptation planning. Many observational constraints have been proposed to reduce the uncertainty of these projections at global to sub-continental scales, but adaptation generally requires detailed, local scale information. Here, we present a temperature-based adaptative emergent constraint strategy combined with data aggregation that reduces the error variance of projected end-of-century changes in annual extremes of daily precipitation under a high emissions scenario by >20% across most areas of the world. These improved projections could benefit nearly 90% of the world's population by permitting better impact assessment and adaptation planning at local levels. Our physically motivated strategy, which considers the thermodynamic and dynamic components of projected extreme precipitation change, exploits the link between global warming and the thermodynamic component of extreme precipitation. Rigorous cross-validation provides strong evidence of its reliability in constraining local extreme precipitation projections.