The heat transfer from a small heating element on a substrate has been investigated numerically. The heating element is positioned at the center of the substrate, and the upper surface of the substrate is cooled by forced convection of the cooling fluid. The computation is performed by using a domain decomposition technique, in which the calculation domain is divided into several zones. It is shown that the temperature of the heating element is mainly controlled by the heat conduction in the substrate near the heating element. On the other hand, the heat transfer to the cooling fluid requires much broader area of the substrate than the size of the heating element. The heat transfer from the substrate to the fluid agrees with the conventional forced-convection correlation of the forced convective heat transfer, but the local conduction-dominated cooling, which determines the peak temperature rise in the system, is relatively unaffected by the flow of the coolant.