Changes in the daily mean surface air temperature distribution between the time periods 1981–2000 and 2081–2100 in 15 climate model simulations participating in the Third Coupled Model Intercomparison Project (CMIP3) are analysed. Variability is defined by first removing the annual cycle after which the range and skewness of the temperature distribution are calculated. Present-day biases for the different aspects of the distribution are also studied, using the ERA-Interim reanalysis as the main reference dataset. The variability in the simulations compared to reanalysis is generally smaller over oceans and larger over land areas. For skewness of the temperature distribution, inter-model variability is much larger and systematic model biases are more local. Model performance regarding the mean values is potentially a good indicator of the model performance for range, but for skewness this relation is weaker. For future changes in the range of daily temperature variability, the models agree best over the Northern Hemisphere mid- to high-latitude land areas, where variability is simulated to decrease. Elsewhere, the inter-model differences are generally larger than the multi-model mean changes. Near the sea ice border, significant negative correlations are found between the changes in mean temperature and the temperature range. For changes in skewness, the signal-to-noise ratio is very low over most areas and no firm conclusions can be drawn from the ensemble results. Our results are relatively insensitive to the precise definition of the range and skewness metrics and to internal variability of climate.