The sensitivity of the climate to CO2 forcing depends on spatially varying radiative feedbacks that act both locally and nonlocally. We assess whether a method employing multiple regression can be used to estimate local and nonlocal radiative feedbacks from internal variability. We test this method on millennial-length simulations performed with six coupled atmosphere–ocean general circulation models (AOGCMs). Given the spatial pattern of warming, the method does quite well at recreating the top-of-atmosphere flux response for most regions of Earth, except over the Southern Ocean where it consistently overestimates the change, leading to an overestimate of the sensitivity. For five of the six models, the method finds that local feedbacks are positive due to cloud processes, balanced by negative nonlocal shortwave cloud feedbacks associated with regions of tropical convection. For four of these models, the magnitudes of both are comparable to the Planck feedback, so that changes in the ratio between them could lead to large changes in climate sensitivity. The positive local feedback explains why observational studies that estimate spatial feedbacks using only local regressions predict an unstable climate. The method implies that sensitivity in these AOGCMs increases over time due to a reduction in the share of warming occurring in tropical convecting regions and the resulting weakening of associated shortwave cloud and longwave clear-sky feedbacks. Our results provide a step toward an observational estimate of time-varying climate sensitivity by demonstrating that many aspects of spatial feedbacks appear to be the same between internal variability and the forced response.