Decadal predictions focus regularly on the predictability of single values, like means or extremes. In this study we investigate the prediction skill of the full underlying surface temperature distributions on global and European scales. We investigate initialized hindcast simulations of the Max Planck Institute Earth system model decadal prediction system and compare the distribution of seasonal daily temperatures with estimates of the climatology and uninitialized historical simulations. In the analysis we show that the initialized prediction system has advantages in particular in the North Atlantic area and allow so to make reliable predictions for the whole temperature spectrum for two to 10 years ahead. We also demonstrate that the capability of initialized climate predictions to predict the temperature distribution depends on the season. Plain Language Summary: The usual way to make statements about temperatures two to 10 years in advance is by using one value. This could be the average, minimum or maximum temperature over some time period. Nevertheless, this simplification hides that this represents only partial information about the full distribution of temperature values. We demonstrate that a climate model is in many areas, especially over and around the North Atlantic, better in predicting the temperature multiple years ahead than assuming a constant climate. We also show that in some areas a climate model, which is starting from a specific point of observations is better than one which does not do that. This shows that it is possible and useful to apply climate predictions to predict the future not only for averages, but for the whole distribution. Key Points: Potential of decadal prediction of temperature distributionsVariability in prediction skill vary regionally over seasonsThe North Atlantic offers an important area where temperature distribution predictability is improved by initialization [ABSTRACT FROM AUTHOR]