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[1] The ongoing increase in extremely warm temperature events across large areas of the globe is generally thought to be a signature of a more extreme climate. However, it is still unclear whether global warming is accompanied by changes in statistical properties beyond the mean, such as an increasing temperature variability. Here we shed light on this issue by uncovering the way probabilities of extremes are being influenced by temperature evolution. Focusing on Europe, we show how the behavior of warm and cold extremes can be determined to a high accuracy by statistically modeling daily temperatures and their changes. Detailed comparison with observations over the past decades puts forward the dominant role of the mean in explaining exceptionally hot events, and rules out contributions from potential changes in second and higher moments.