This paper analyses the probabilistic future behaviour of heat-waves (HWs) in the city of Madrid in the twenty-first century, using maximum daily temperatures from twenty-one climate circulation models under two representative concentration pathways (RCP 8.5 & RCP 4.5). HWs are modelled considering three factors: number per annum, duration and intensity, characterised by three stochastic processes: Poisson, Gamma and truncated Gaussian, respectively. Potential correlations between these processes are also considered. The probabilistic temperature behaviour is combined with an epidemiological model with stochastic mortality risk following a generalized extreme value distribution (gev). The objective of this study is to obtain probability distributions of mortality and risk measures such as the mean value of the 5% of worst cases in the 21st century, in particular from 2025 to 2100. Estimates from stochastic models for characterising HWs and epidemiological impacts on human health can vary from one climate model to another, so relying on a single climate model can be problematic. For this reason, the calculations are carried out for 21 models and the average of the results is obtained. A sensitivity adaptation analysis is also performed. Under RCP 8.5 for 2100 for Madrid city a mean excess of 3.6 °C over the 38 °C temperature threshold is expected as the average of all models, with an expected attributable mortality of 1614 people, but these figures may be substantially exceeded in some cases if the highest-risk cases occur.