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The increased exposure of human populations to heat stress is one of the likely consequences of global warming, and it has detrimental effects on health and labor capacity. Here, we consider the evolution of heat stress under climate change using 21 general circulation models (GCMs). Three heat stress indicators, based on both temperature and humidity conditions, are used to investigate present-day model biases and spreads in future climate projections. Present day estimates of heat stress indicators from observational data shows that humid tropical areas tend to experience more frequent heat stress than other regions do, with a total frequency of heat stress 250–300 d yr⁻¹. The most severe heat stress is found in the Sahel and south India. Present-day GCM simulations tend to underestimate heat stress over the tropics due to dry and cold model biases. The model based estimates are in better agreement with observation in mid to high latitudes, but this is due to compensating errors in humidity and temperature. The severity of heat stress is projected to increase by the end of the century under climate change scenario RCP8.5, reaching unprecedented levels in some regions compared with observations. An analysis of the different factors contributing to the total spread of projected heat stress shows that spread is primarily driven by the choice of GCMs rather than the choice of indicators, even when the simulated indicators are bias-corrected. This supports the utility of the multi-model ensemble approach to assess the impacts of climate change on heat stress.