First, less than 30 g of brown coal packed in a sphere stainless net and placed in an air naturally circulating temperature-programmed oven was found to start spontaneous combustion from the center of the coal sphere when the oven temperature was raised to 135 degrees C. This was because the heat generation rate by the oxidation of coal was larger than the rate of heat dissipation rate by natural convection at 135 degrees C. Next, to clarify the mechanism by which coal is heated to 135 degrees C, the temperature increase of less than 10 g of the fixed bed of dried brown coal was measured by contacting the coal with flowing dry air or wet air at 50, 70, 95, and 107 degrees C. It was found that the maximum temperature increase in the dry air was almost null at 70 degrees C and only 5 degrees C or so even at 107 degrees C. On the other hand, the maximum temperature increases were respectively 10, 25, 46, and 40 degrees C at 50, 70, 9S, and 107 degrees C in the wet air, suggesting that the adsorption of water vapor plays a crucial role in increasing the coal temperature high enough for the spontaneous combustion to start. A simple simulation program was developed for expressing the temperature change observed by the above fixed bed experiment by formulating the mass and enthalpy balance equations with the separately measured heat generation rate by the coal-oxygen interaction at 50-150 degrees C and the adsorption isotherm and the heat of adsorption of water vapor on coal at 70 degrees C. The simulation program well expressed the temperature change for the experiments performed at 70 degrees C in both the wet air and the dry air, indicating that the spontaneous heating of coal is brought about by the coupled effect of the adsorption of water vapor and the coal oxygen interaction. In addition, the simulation showed how the spontaneous combustion of coal starts in the wet air.