Spatial patterns of the standard deviation and skewness of daily and monthly mean summer temperature were studied with the climate model Institute of Numerical Mathematics Climate Model version 4 for three scenarios: simulation of the preindustrial climate, effect of quadrupling CO2 concentrations, and simulation of transient climate change for the period 1850–2100. In high skewness regions of the simulated preindustrial climate, hot periods exceeded the number expected for a normal distribution by a factor of 2–8. In the model in which CO2 concentrations were quadrupled, we found an increase in standard deviation and a northward shift of the area with positive skewness compared with the preindustrial scenario. The maximum increase in summer mean temperature was found in subtropical areas. The maximum increase in temperature averaged over the warmest 30 % of days was about 500 km to the north of the region of maximum increase of seasonal mean temperature, in the area where standard deviation was increased. The maximum increase in temperature averaged over the warmest 0.1 % of days was 500 km further north again, in an area of increased skewness. In the transient climate change simulation for 1850–2100, there was a noticeable increase in temperature of the warmest days exceeding the summer mean temperature in regions with increased skewness. In regions with decreased skewness, there was only a small increase or no rise at all in temperature for the warmest days under transient global warming.