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Extratropical eddy-driven jets are predicted to shift poleward in a warmer climate. Recent studies have suggested that cloud radiative effects (CRE) may enhance the amplitude of such shifts. But there is still considerable uncertainty about the underlying mechanisms, whereby CRE govern the jet response to climate change. This study provides new insights into the role of CRE in the jet response to climate change by exploiting the output from six global warming simulations run with and without atmospheric CRE (ACRE). Consistent with previous studies, it is found that the magnitude of the jet shift under climate change is substantially increased in simulations run with ACRE. It is hypothesized that ACRE enhance the jet response to climate change by increasing the upper-tropospheric baroclinicity due to the radiative effects of rising high clouds. The lifting of the tropopause and high clouds in response to surface warming arises from the thermodynamic constraints placed on water vapor concentrations. Hence, the influence of ACRE on the jet shift in climate change simulations may be viewed as an additional "robust'' thermodynamic constraint placed on climate change by the Clausius-Clapeyron relation. The hypothesis is tested in simulations run with an idealized dry GCM, in which the model is perturbed with a thermal forcing that resembles the ACRE response to surface warming. It is demonstrated that 1) the enhanced jet shifts found in climate change simulations run with ACRE are consistent with the atmospheric response to the radiative warming associated with rising high clouds, and 2) the amplitude of the jet shift scales linearly with the amplitude of the ACRE forcing.