In weather and climate applications, a wide range of commonly employed heatwave intensity indices relies either on cumulative or averaged values of temperature-based variables. In this study, by comparing four different heatwave intensity indices applied to reanalysis data we show that metrics based on cumulative or averaged values lead to important differences in the detection of the most intense events of the period 1950–2021. This suggests that particular attention is needed when using the two families of metrics for assessing heatwave intensity. Indices based on cumulative values should be preferred over the ones relying on temporal averages, better allowing for the comparison of events of different length. Under these considerations, one of the considered cumulative indices is used for characterizing heatwaves of the period 1950–2021, showing that heatwaves that were unlikely before 1986 have become almost 10 times more frequent and up to three times more intense during recent times.