A fundamental aspect of greenhouse-gas-induced warming is a global-scale increase in absolute humidity. Under continued warming, this response has been shown to pose increasingly severe limitations on human activity in tropical and mid-latitudes during peak months of heat stress. One heat-stress metric with broad occupational health applications is wet-bulb globe temperature. We combine wet-bulb globe temperatures from global climate historical reanalysis and Earth System Model (ESM2M) projections with industrial and military guidelines for an acclimated individual's occupational capacity to safely perform sustained labour under environmental heat stress (labour capacity)--here defined as a global population-weighted metric temporally fixed at the 2010 distribution. We estimate that environmental heat stress has reduced labour capacity to 90% in peak months over the past few decades. ESM2M projects labour capacity reduction to 80% in peak months by 2050. Under the highest scenario considered (Representative Concentration Pathway 8.5), ESM2M projects labour capacity reduction to less than 40% by 2200 in peak months, with most tropical and mid-latitudes experiencing extreme climatological heat stress. Uncertainties and caveats associated with these projections include climate sensitivity, climate warming patterns, CO2 emissions, future population distributions, and technological and societal change.