The severity of warming predicted by climate models depends on their transient climate response (TCR). The intermodel TCR spread has persisted at ~100 % of its average for decades. Existing observational TCR constraints are based on the observed historical warming response to historical forcing, and their uncertainty spread is equally wide, mainly due to uncertainty in forcing, particularly aerosols. In contrast, no aerosols are involved in the forcing of the solar cycle, providing an independent, tighter constraint. Here, we define a climate sensitivity metric: the time-dependent response regressed against the time-dependent forcing, allowing phenomena with distinct temporal variations, such as the solar cycle with 11-year cyclic forcing, to be used to constrain the TCR, which has a linear time-dependent forcing. We find a theoretical linear relationship between them. (More on nature.com)