Heat generated in electronic devices has to be effectively removed because excessive temperature strongly impairs their performance and reliability. Embedding a high thermal conductivity network into an electronic device is an effective method to conduct the generated heat to the outside. In this study, inspired by the pinnate leaf, we present a pinnate leaf-like network embedded in the matrix (i.e., electronic device) to cool the matrix by conduction and develop a method to construct the optimal network. In this method, we first investigate the effect of the matrix thickness on the conductive cooling performance of the network, and then optimize the network architecture from a global perspective so that to minimize the maximum temperature difference between the heat sink and the matrix. The results indicate that the matrix thickness determines the optimal distance of the neighboring collection channels in the network, which minimizes the maximum temperature difference between the matrix and the network, and that the optimal network greatly reduces the maximum temperature difference in the network. The results can serve as a design guide for efficient conductive cooling of electronic devices. (C) 2014 Elsevier Ltd. All rights reserved.