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Urban heat islands (UHIs) exacerbate the risk of heat-related mortality associated with global climate change. The intensity of UHIs varies with population size and mean annual precipitation, but a unifying explanation for this variation is lacking, and there are no geographically targeted guidelines for heat mitigation. Here we analyse summertime differences between urban and rural surface temperatures (Delta T-s) worldwide and find a nonlinear increase in Delta T-s with precipitation that is controlled by water or energy limitations on evapotranspiration and that modulates the scaling of Delta T-s with city size. We introduce a coarse-grained model that links population, background climate, and UHI intensity, and show that urban-rural differences in evapotranspiration and convection efficiency are the main determinants of warming. The direct implication of these nonlinearities is that mitigation strategies aimed at increasing green cover and albedo are more efficient in dry regions, whereas the challenge of cooling tropical cities will require innovative solutions.