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We quantify the long-term predictability of global mean daily temperature data by means of the R&#233;nyi entropy of second order <i>K₂</i>. 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 <i>K₂</i> 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&deg; resolution, Mitchell et al., 2005)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 <i>K₂</i> with the linear variance of the temperature data.