Nowadays, production of Small-Scale electronic pieces has been developed and necessity of investigation on cooling and strength of these parts is crucial. Generating internal heat in these parts causes temperature increases severely. As a consequence, some stresses induced by thermal expansion form and then capability and strength of them to reduce. It can be said that thermal management and mechanical strength are the main factors of advanced electronic packages. In this research, based on constructal theory, steady-state heat transfer in order to cool a disk as well as all generated stresses due to thermal expansion of the disc were investigated by mean of some inserts with high coefficient of thermal conductivity. Here, three types of branching configurations on the disc which are called radial, dendritic with one pairing level, and dendritic with two pairing levels were studied. These were done by numerically calculation of maximum temperature and stress of the disc and then optimization of the configurations. This procedure is followed by adding the number of inserts which leads to a considerable decrease in maximum temperature. When 16 inserts were embedded in the disc, Maximum stresses became minimal. This procedure was carried out by the changes in geometrical parameters of dendritic design.They include variation of longitudinal parameters of inserts and angles between them. So maximum value of temperature and stress were calculated and minimized. It was observed that there is a close relation between maximum temperature and stress in the disc. It means that as the distribution of inserts in the structure was uniform i.e., they could access to each point of the disc, both of maximum temperature and stress were reduced. Furthermore, by Changing the structure from radial to dendritic with one pairing level caused a decrease in the maximum temperature and stress up to 17% and 3.2%, respectively. Results showed that changing the structure from dendritic with one pairing level to dendritic with two pairing levels, rendered a decrease in the maximum temperature up to5.6% and an increase in the maximum stress up to 1% as well. Keywords: Constructal theory, Cooling and Mechanical strength, Thermal Stress, Radial and Dendritic design.