The response of extreme precipitation to warming varies widely among climate models, especially in the tropics. In some models, there have been indications that the rate of response increases with warming—that the response is not linear. We investigate the evolution of extreme precipitation, quantified by the maximum accumulated precipitation in a day each year, in CESM1. We find that tropical‐ and global‐average extreme precipitation is related to global‐mean surface temperature quadratically. This behavior is associated with an increase in the large‐scale fraction of extreme precipitation and also strengthening circulation on extreme precipitation days. Compared to other CMIP5 models, the nonlinearity in CESM1 is among the largest. One implication is that the difference between CESM1 simulations with full forcing and with fixed aerosols cannot be used to isolate the response of extreme precipitation to aerosols, as the resulting climates are not equally warm.