Irrigation and urban greening can mitigate extreme temperatures and reduce adverse health impacts from heat. However, some recent studies suggest these interventions could actually exacerbate heat stress by increasing humidity. These studies use different heat stress indices (HSIs), hindering intercomparisons of the relative roles of temperature and humidity. Our method uses calculus of variations to compare the sensitivity of HSIs to temperature and humidity, independent of HSI units. We explain the properties of different HSIs and identify conditions under which they disagree. We highlight recent studies where the use of different HSIs could have led to opposite conclusions. Our findings have significant implications for the evaluation of irrigation and urban greening as adaptive responses to overheating and climate adaptation measures in general. We urge researchers to be critical in their choice of HSIs, especially in relation to health outcomes; our method provides a useful tool for making informed comparisons.