The response of tropical cyclone (TC) frequency to sea surface warming is uncertain in climate models. We hypothesize that one source of uncertainty is the anomalies of large-scale atmospheric radiation under climate change, and we investigate the influence on TC frequency. Given two atmospheric models with opposite TC frequency response to uniform sea surface warming, we interchange their atmospheric radiation anomalies in experiments with prescribed radiative heating rates. The largest model discrepancy occurs in the Western North Pacific, where the TC frequency tends to increase with anomalous large-scale ascent caused by prescribed positive radiation anomalies; while the TC frequency tends to decrease with anomalous large-scale descent caused by prescribed negative radiation anomalies. The model spread in TC frequency response is approximated by the model spread in the frequency response of pre-TC vortices (seeds), which is explained by changes in the large-scale circulation using a downscaling formula known as the seed propensity index. We further generalize the index to predict the influence of large-scale radiation anomalies on TC seed frequency. The results show that model spread in TC and seed frequency response can be reduced when constraining the large-scale radiation anomalies.