Two main mechanisms can potentially explain the spread in the magnitude of global warming simulated by climate models: deep ocean heat uptake and climate feedbacks. Here, we show that deep oceanic heat uptake is a major source of spread in simulations of 21st century climate change. Models with deeper baseline polar mixed layers are associated with larger deep ocean warming and smaller global surface warming. Based on this result, we set forth an observational constraint on polar vertical oceanic mixing. This constraint suggests that many models may overestimate the efficiency of polar oceanic mixing and therefore may underestimate future surface warming. Thus to reduce climate change uncertainties at time-scales relevant for policy-making, improved understanding and modelling of oceanic mixing at high latitudes is crucial.