In recent years, it has been proposed that multi-scale numerical analyses can be applied to structural design to reduce experimental efforts. Although many multi-scale analyses have been mainly applied to mechanical dynamics, they do not approach the subject from a thermal perspective, which is a very important phenomenon for structural design. With this consideration, in this paper we dealt with the formulation and programming of the unsteady-state heat transfer problem by a mesh superposition method, which is spotlighted in the stress analysis field. The numerical results of the proposed method have good agreement with the conventional finite element method. It has also been verified that the developed program has good accuracy and that the proposed method is useful in the design of engineering products.