The steady increase in greenhouse gas concentrations is inducing a detectable rise in global temperatures. The sensitivity of human societies to warming temperatures is, however, a transcendental question not comprehensively addressed to date. Here we show the link between temperature, humidity and daily numbers of deaths in nearly 200 European regions, which are subsequently used to infer transient projections of mortality under state-of-the-art high-resolution greenhouse gas scenario simulations. Our analyses point to a change in the seasonality of mortality, with maximum monthly incidence progressively shifting from winter to summer. The results also show that the rise in heat-related mortality will start to completely compensate the reduction of deaths from cold during the second half of the century, amounting to an average drop in human lifespan of up 3-4 months in 2070-2100. Nevertheless, projections suggest that human lifespan might indeed increase if a substantial degree of adaptation to warm temperatures takes place.