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Extreme precipitation events are projected to intensify with global warming, threatening ecosystems and amplifying flood risks. However, observation-based estimates of extreme precipitation-temperature (EP-T) sensitivities show systematic spatio-temporal variability, with predominantly negative sensitivities across warmer regions. Here, we attribute this variability to confounding cloud radiative effects, which cool surfaces during rainfall, introducing covariation between rainfall and temperature beyond temperature’s effect on atmospheric moisture-holding capacity. We remove this effect using a thermodynamically constrained surface-energy balance, and find positive EP-T sensitivities across continents, consistent with theoretical arguments. Median EP-T sensitivities across observations shift from −4.9%/°C to 6.1%/°C in the tropics and −0.5%/°C to 2.8%/°C in mid-latitudes. Regional variability in estimated sensitivities is reduced by more than 40% in tropics and about 30% in mid and high latitudes. Our findings imply that projected intensification of extreme rainfall with temperature is consistent with observations across continents, after confounding radiative effect of clouds is accounted for.