Global warming is projected to intensify during the twenty-first century. Yet, only few studies investigate how global warming could be perceived by future populations. Here, we propose an assessment of how climate change could be perceived by combining climatological indicators. We analyse extremes of temperature (T-99) and simplified Wet-Bulb Globe Temperature (WBGT(99)), a heat stress index assessing the combined effect of elevated temperature and humidity on the human body. The speed of change is defined for each year as the difference between the previous 20 years and the twenty upcoming years (i.e. with a moving baseline), and we assess how these speeds emerge from each last 20-year interannual variability. Using a set of 12 CMIP5 models, speeds of change ofT(99)and WBGT(99)in 2080 are both twice as fast compared with current speeds in mid-latitudes, and by up to four times faster in the tropics under the RCP8.5 scenario. Warming accelerations are thus similar forT(99)and WBGT(99). However, these speeds in tropical regions in 2080 are projected to be 2.3 times larger than the last 20-year interannual variability for WBGT(99), and only 1.5 to 1.8 times larger forT(99). According to the models, the WBGT(99)intensification will be more emergent from the recent year-to-year variability than theT(99)warming. This analysis suggests that the accelerated warming of heat extremes will be felt more strongly by populations than current changes for RCP8.5, and that this evolution will be more perceived in heat stress than in temperature, particularly within the tropics.