Extreme heat, particularly if combined with humidity, poses a severe risk to human health. To estimate future global risk of extreme heat with humidity on health, we calculate indicators of heat stress that have been commonly used; the Heat Index, the Wet-Bulb Globe Temperature and the Wet-Bulb Temperature, from the latest Climate Model Intercomparison Project (CMIP6) projections. We analyze how and where different levels of heat stress hazards will change, from severe to deadly, and how results are sensitive to the choice of the index used. We evaluate this risk at country-level and use population and GDP growth scenario to estimate the vulnerability of each nation. Consistent with previous studies, we find that South and East Asia, and the Middle-East, are highly exposed to heat stress hazards, and that this exposure increases by 20\% to 60\% with global mean temperature change from 1.5 to 3 degrees Celsius. However, we also find substantial increases in heat health risk for some vulnerable countries with less adaptive capacity, such as West Africa, and Central and South America. For these regions, about 20 to more than 50\% of the population could be exposed to severe heat stress each year on average, independent of the index used. For global warming of 3 degrees, European countries and the USA will also be exposed several times per year to conditions with daily mean heat stress level equal to the maximum heat stress of the 2003 heat wave.