We introduce system identification techniques to climate science wherein multiple dynamic input–output relationships can be simultaneously characterized in a single simulation. This method, involving multiple small perturbations (in space and time) of an input field while monitoring output fields to quantify responses, allows for identification of different timescales of climate response to forcing without substantially pushing the climate far away from a steady state. We use this technique to determine the steady-state responses of low cloud fraction and latent heat flux to heating perturbations over 22 regions spanning Earth's oceans. We show that the response characteristics are similar to those of step-change simulations, but in this new method the responses for 22 regions can be characterized simultaneously. Furthermore, we can estimate the timescale over which the steady-state response emerges. The proposed methodology could be useful for a wide variety of purposes in climate science, including characterization of teleconnections and uncertainty quantification to identify the effects of climate model tuning parameters.