We present a new approach to modeling the future development of extreme temperatures globally and on the time-scale of several centuries by using non-stationary generalized extreme value distributions in combination with logistic functions. The statistical models we propose are applied to annual maxima of daily temperature data from fully coupled climate models spanning the years 1850 through 2300. They enable us to investigate how extremes will change depending on the geographic location not only in terms of the magnitude, but also in terms of the timing of the changes. We find that in general, changes in extremes are stronger and more rapid over land masses than over oceans. In addition, our statistical models allow for changes in the different parameters of the fitted generalized extreme value distributions (a location, a scale and a shape parameter) to take place independently and at varying time periods. Different statistical models are presented and the Bayesian Information Criterion is used for model selection. It turns out that in most regions, changes in mean and variance take place simultaneously while the shape parameter of the distribution is predicted to stay constant. In the Arctic region, however, a different picture emerges: There, climate variability is predicted to increase rather quickly in the second half of the twenty-first century, probably due to the melting of ice, whereas changes in the mean values take longer and come into effect later.