Present-day land temperatures simulated by state-of-the-art global climate models exhibit considerable uncertainty. Generally it is assumed that these temperature biases do not affect the projected warming in response to rising greenhouse gas concentrations (i.e. drop out by subtracting projected and present-day temperatures), but for specific regions and seasons this assumption is invalid. Here we show that, on the contrary, for large continental regions, such as Europe, state-of-the art global climate models with a warm summer bias project a relatively strong warming. This is because continental summer temperatures depend chiefly on soil drying in response to spring and summer solar radiation increase: models that dry fastest (due to the interaction of clouds, convection and soil hydrology) exhibit the strongest reductions in evaporation and consequently a more pronounced end-of-summer warming. These physical mechanisms acting on a seasonal timescale also govern the long-term climate response to greenhouse forcing over continental regions in summer. Combining these findings, we use the current model biases to reduce the uncertainty range in the projected warming over Europe from 3.6–8.6 °C to 4.6–7.3 °C (a reduction of about 50%). Given the huge potential impacts of the warmest projections on health, agriculture and water management, constraining the range of future summer climate change is imperative for relevant mitigation and adaptation strategies.