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In a global warming regime, particular attention must be paid to possible changes in prolonged temperature extreme events on the regional scale, due to their strong impacts. But, while the increase in mean temperature is statistically significant and unequivocal, we do not know if the behaviour of extreme events is another significant signal of climate change or if it is still compatible with a "constant climate", that is, with a stationary distribution of temperatures. Here, we propose a method to study the extremes through the analysis of the trend of the new historical records of mean monthly temperatures, and apply it to data about Italy, a country affected by a warming stronger than the global mean. A deep analysis of a 56-year data set for 54 Italian stations and the use of Monte-Carlo simulations permits us to achieve the evidence of a climate change also from the analysis of extremes. This analysis is performed at both the national level and for clusters of stations. The results show that the number of warm records increases more than what is expected by a constant climate "law," in some months reaching or even overpassing the 95th percentile: May, June, July, and especially August appear as the most significant in this respect. Vice versa, the number of cold records lies often close to the fifth percentile or even under it; furthermore, in many months the cold records are very few after the middle of the 1990s. Some months can be, however, seen as "stationary islands." For instance, the behaviour of the number of warm records in December and January follows closely the hypothesis of a constant climate, even if, in contrast, the cold records in January lie under the fifth percentile.