Changes in characteristics of the distribution of temperature, in addition to shifts towards warmer temperatures, can have substantial implications for society and the environment. A change in shape, for example, can be caused by differences in the rates of warming of cold and warm extremes relative to average temperatures. These rates of warming vary both spatially and temporally, with strong geographic and seasonal differences in how local extremes are changing relative to local average temperatures. In this paper, we investigate how seasonal warm and cold tails of both daily maximum and minimum temperatures are changing relative to corresponding seasonal mean temperatures. Analysing gridded observations over land areas and climate models from the CMIP5 archive, we show that in recent decades, the greatest differences between warming rates of extremes and the mean occur in the cold tails of the distribution for many regions in the Northern Hemisphere extratropics during all seasons except boreal summer. Globally, June through August show the smallest differences between extremes and mean warming rates. While the climate models show relatively low spatial correlations in their change patterns with each other as well as the observations for past decades, future simulated changes are shown to be systematic and robust, with a clear signal in the warming of extremes relative to the mean. The strongest differences between warming rates of extremes and the mean are projected for Northern Hemisphere mid‐ to high‐latitude regions, where the cold tails warm more than the average for all seasons except boreal summer. This is especially widespread in autumn and spring, where the models predict cold extremes to warm at least 3°C more than mean temperatures for much of the Northern Hemisphere extratropics. The results presented here highlight the importance of considering all aspects of the distribution when analysing changes in temperature.