Abstract Climate responses to global warming exhibit large dependence on the spatial pattern of sea surface temperature (SST) changes. A Green’s function (GF) approach—predicting the global climate response to a complex SST pattern change as the linear superposition of the response to finite-area SST perturbations evaluated in isolation—has been used to systematically evaluate and understand the top of atmosphere (TOA) radiation response to patterned warming. However, in general, the linear GF approach fails for TOA radiation reconstruction under future global warming scenarios in coupled models. Here, we show that the linear superposition of global mean TOA radiation responses to large SST warming perturbations at multiple patches (the GF approach prediction) overestimates the actual response to simultaneous multipatch perturbation. This is because the linear superposition overestimates tropical large-scale convection aggregation strengthening upon localized heating that enhances longwave radiative cooling, which is further explained by the overestimation of circulation response and associated horizontal water vapor transport. The nonadditivity of TOA radiation response is caused by the nonadditivity of convection aggregation, ultimately rooted in nonlinear tropical dynamics. We also demonstrate that the prediction error of the GF approach grows with decreasing patch size (equivalently, increasing patch number). We conclude that using the GF approach to predict future climate change could overestimate longwave radiative cooling and underestimate (effective) climate sensitivity. Numerical experiments may be used to identify specific perturbation patterns where the errors are smaller than the signal. Our research also highlights that an increase in the degree of large-scale convection aggregation has a nonlinear and negative feedback for mean warming.