In order to eliminate a cooling system from an internal combustion engine, we studied structures to reduce heat rejection from a combustion chamber. It was known to be very difficult to increase the heat-insulation rate of a low heat-rejection engine with a coated combustion chamber wall with a zirconia layer to more than 50%. Therefore a heat flux and temperatures were calculated by using the finite-element method in order to develop a new structure for a low heat rejection engine. The calculation results were compared with the temperatures measured in the engine which was fabricated with a silicon nitride combustion chamber wall incorporated in a heat-insulation structure composed of an air gap and a gasket of very low thermal conductivity. The result was that the compound heat-insulation structure was very effective in reducing heat rejection from the combustion chamber wall to the outer cylinder made of cast iron. It was also confirmed that the temperature distributions calculated by F.E.M. correlated nicely with the measured temperature data of the engine if the adjustment was made to the heat transfer coefficient by multiplying a large number to the one for the combustion chamber wall contacting a burning flame and a small number to the one for the wall contacting a gas after burning.