In general, biases of climate models depend upon the climate state (i.e., are nonstationary). Recent studies have shown that the adoption of a stationary temperature bias can lead to an overestimation of projected summer warming in southern Europe. It has also been proposed to use a bias correction that increases linearly with temperature. While such an assumption is well-justified for near-term projections, one wonders whether and at what temperature this relation levels off if it does. Here we show, using regional climate model simulations of the ENSEMBLES project and from a single-model perturbed physics ensemble, that the linear bias assumption breaks down at high model temperatures, followed by a transition to a constant bias relation. This transition is apparent in strongly biased model simulations and supported using a pseudo-reality approach. We show that soil moisture scarcity explains a large degree of summer temperature biases across both ensembles and that the limits of soil moisture depletion are responsible for the transition. A linear temperature bias correction therefore potentially over-corrects summer warming, and implicitly assumes unphysical relations between soil moisture and temperature, in particular when considering high-emission scenarios. We conclude that a physically consistent and time-dependent temperature bias correction considering the state of the soil would increase the robustness of bias correction and reduce the uncertainty of 21st century summer warming.