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The persistent inter‐model spread in the response of global‐mean surface temperature to increased CO2 (known as the "Equilibrium Climate Sensitivity," or "ECS") is a crucial problem across model generations. This work examines the influence of the models' present‐day atmospheric circulation climatologies, and the accompanying climatological cloud radiative effects, in explaining that spread. We analyze the Coupled Model Intercomparison Project Phase 6 (CMIP6) models and find that they simulate a more poleward, and thus more realistic, edge of the Hadley cell (HC) in the Southern Hemisphere than the CMIP5 models, although the climatological shortwave cloud radiative effects are similar in the two generations of models. A few CMIP5 models with extreme equatorward biases in the HC edge exhibited high ECS due to strong Southern midlatitude shortwave cloud radiative warming in response to climate change, suggesting an ECS dependence on HC position. We find that such constraint no longer holds for the CMIP6 models, due to the absence of models with extreme HC climatologies. In spite of this, however, the CMIP6 models show an increased spread in ECS, with more models in the high ECS range. In addition, an improved representation of the climatological jet dynamics does not lead to a new emergent constraint in the CMIP6 models either. [ABSTRACT FROM AUTHOR]