Planning for adaptation to climate change requires accurate climate projections. Recent studies have shown that the uncertainty in global mean surface temperature projections can be considerably reduced by using historical observations. However, the transposition of these new results to the local scale is not yet available. Here we adapt an innovative statistical method that combines the latest generation of climate model simulations, global observations, and local observations to reduce uncertainty in local temperature projections. By taking advantage of the tight links between local and global temperature, we can derive the local implications of global constraints. The model uncertainty is reduced by 30% up to 50% at any location worldwide, allowing to substantially improve the quantification of risks associated with future climate change. A rigorous evaluation of these results within a perfect model framework indicates a robust skill, leading to a high confidence in our constrained climate projections.