A two-dimensional (axisymmetric) transient heat conduction in components computer program (HCC) was successfully developed for predicting engine combustion chamber wall temperatures. The alternating direction explicit (ADE) Saul＇yev method, an explicit, unconditionally stable finite difference method, was used in the code. Special treatments for the head gasket and the piston-liner air gap, the piston movement, and a grid transformation for describing the realistic piston bowl shape were designed and utilized. The results were compared with a finite element method and were verified to be accurate for simplified test problems. In addition, the method was applied to realistic problems of heat transfer in an Isuzu engine and a Caterpillar diesel engine, and gave good agreement with available experimental measurements.