This thesis deals with the analysis of return times of heat extremes in different climate scenarios. With the help of the coupled climate model AWI-ESM2.1, the historical climate since 1850 and the two future scenarios SSP1-2.6 and SSP5-8.5 are simulated. A small ensemble of simulations is calculated in each case. The daily maximum temperatures are analyzed using two methods from extreme value theory: the block maxima method and the peaks-over-threshold method. The average return times of different temperatures are calculated from the associated distribution functions. The Kolmogorov-Smirnov test shows that the data can be well described by both the generalized extreme value distribution (Weinbull distribution) and the Pareto distribution. However, due to the autocorrelation of the temperatures, the block maxima method proved to be more suitable for estimating the return times. The temperatures associated with a certain return time have already risen since the pre-industrial age and there is a strong dependence on the future scenario considered. In order to better understand the influence of the autocorrelation, the distribution of the return times for a constant temperature threshold is also examined. If the correlation is weak, as is the case in Germany, for example, the distribution can be described by an exponential function. In other places such as South America and Indonesia, the temperatures are more strongly correlated, the autocorrelation of the temperature differences to the average annual course initially falls off according to the power law. As a result, both very short and very long return times are becoming more frequent. An equation taken from the literature for the distribution of return times in long-term correlated systems is verified using the simulated daily maximum temperatures.