Climatic warming of about 0.5 ° C in the global mean since the 1970s has strongly increased the occurrence-probability of heat extremes on monthly to seasonal time scales. For the 21st century, climate models predict more substantial warming. Here we show that the multi-model mean of the CMIP5 (Coupled Model Intercomparison Project) climate models accurately reproduces the evolution over time and spatial patterns of the historically observed increase in monthly heat extremes.