Heatwaves are one of the leading causes of climate-induced mortality. Using the examples of recent heatwaves in Europe, the United States and Asia, we illustrate how the communication of dangerous conditions based on temperature maps alone can lead to insufficient societal perception of health risks. Comparison of maximum daily values of temperature with physiological heat stress indices accounting for impacts of both temperature and humidity, illustrates substantial differences in geographical extent and timing of their respective peak values during these recent events. This signals the need to revisit how meteorological heatwaves and their expected impacts are communicated. Close collaboration between climate and medical communities is needed to select the best heat stress indicators, establish them operationally, and introduce them to the public. npj Climate and Atmospheric Science (2023) 6:33.