Precipitation is expected to increase in a warmer global climate, yet how sensitive precipitation is to warming depends on poorly constrained cloud radiative processes. Clouds respond to surface warming in ways that alter the atmosphere's ability to radiatively cool and hence form precipitation. Here we examine the links between cloud responses to warming, atmospheric radiative fluxes, and hydrological sensitivity in AMIP6 simulations. The clearest impacts come from high clouds, which reduce atmospheric radiative cooling as they rise in altitude in response to surface warming. Using cloud locking, we demonstrate that high cloud radiative changes weaken Earth's hydrological sensitivity to surface warming. The total impact of cloud radiative effects on hydrological sensitivity is halved by interactions between cloud and clear-sky radiative effects, yet is sufficiently large to be a major source of uncertainty in hydrological sensitivity.