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Abstract The climate response to the Mt. Pinatubo volcanic eruption is analyzed using large ensembles of Coupled Model Intercomparison Project Phase 6 (CMIP6) historical simulations. In contrast to previous work, we find that standard measures of the global temperature response to volcanic forcing are not significantly correlated with climate sensitivity across models. Isolating the shortwave response due to non‐cloud effects does not improve the correlation with climate sensitivity. Earlier constraints on climate sensitivity based on the response to Mt. Pinatubo are consistent with having arisen by chance because of the small size of the ensembles used. Our results suggest that the response to Mt. Pinatubo cannot be used to constrain the climate sensitivity to increased greenhouse gas concentrations, as has been proposed, because the radiative feedbacks in response to volcanic eruptions are not well correlated with the feedbacks governing the long‐term response to greenhouse gas forcing.