This study applies the constructal design method to obtain the configuration that provides the easier access to the heat flowing through an I-shaped high conductive pathway which is inserted into a volumetric medium with low thermal conductivity and heat-generating. A third material separates the high conductive material from the heat-generating medium representing the thermal contact resistance. The body is cooled by an isothermal heat sink with low temperature which is located in the rim. The objective consists in discovering configurations that facilitates the heat flow diminishing the maximal excess of temperature independent of the place where it is located. The total volume and the volume of high conductivity material are fixed, but their aspect ratio can vary. The results indicate that the thermal contact resistance is larger when thermal conductivity of the high conductivity material and the thermal conductivity of the material that represents the thermal contact resistance are smaller. It can increase the maximal dimensionless excess of temperature and the optimal aspect ratio by approximately 56% and 17% respectively, In addition, varying the external ratio can increase the maximum dimensionless temperature almost 20% taking into account the thermal contact resistance. However, changes in this ratio had almost no effect on the optimal geometry of the I-shaped high thermal conductivity pathway. (C) 2015 Elsevier Ltd. All rights reserved.