External climatic conditions such as outdoor air temperature and solar radiation fluctuate randomly with time, and cause the random fluctuation of room air temperature, humidity and heating load. So far, the authors have presented a method which analyzed the stochastic properties of room air temperature, humidity and heating load provided that the probability distribution of the external parameters is Gaussian (Normal). In this paper, a new method is proposed which gives the probability density function of room air temperature and heating load taking account of non-Gaussian external climates. This method is a simple extension to the second-order analysis already shown in previous papers. A thermal system composed of one mass is used to analyze the relationship between the eigenvalue of the system and the degree of non-Gaussianity. Next, the similar calculation using a simple room clarifies the influence of non-Gaussianity on room air temperature and heating load. The utility of the previously proposed thermal calculation method, which gives only the mean and variance of the heating load, is discussed through comparison with the present results.