A methodology is presented for investigating the uncertainty properties of the building thermal processes caused by the random behaviour of the meteorological processes and the casual gains. A detailed building thermal model is used with a stochastic weather model and a random casual gain model. The probability distribution of the zone temperature of the building is calculated directly from these models. The overheating risk has been analysed as an example. The probability distribution of the periods when the zone temperature is higher than the demand temperature is calculated. The result shows all the possible situations rather than only a sample as would be obtained by running a normal simulation using given weather data. The influence of different building components on the overheating risk has been studied. The result shows that the most likely component for overheating risk in a residential building in Beijing is the window size. The thermal mass of the internal walls and the placing of windows have little effect on overheating risk.