We quantify the long-term predictability of global mean daily temperature data by means of the Rényi entropy of second order K2. We are interested in the yearly amplitude fluctuations of the temperature. Hence, the data are low-pass filtered. The obtained oscillatory signal has a more or less constant frequency, depending on the geographical coordinates, but its amplitude fluctuates irregularly. Our estimate of K2 quantifies the complexity of these amplitude fluctuations. We compare the results obtained for the CRU data set (interpolated measured temperature in the years 1901-2003 with 0.5° resolution, Mitchell et al., 20051) with the ones obtained for the temperature data from a coupled ocean-atmosphere global circulation model (AOGCM, calculated at DKRZ). Furthermore, we compare the results obtained by means of K2 with the linear variance of the temperature data.