Optimization of a highly conductive insert embedded into a heated rectangular chip has been lately investigated. The role of the insert was to gather the heat current within the chip body and remove it to a minimum temperature heat sink. The central goal of this paper is to invoke several reconsiderations, which result in excessive reduction of the peak temperature in the heated chip in comparison with the lowest peak temperature existed in the archival literature. It is proved that for the configuration under study with its bottom surface receiving a heat flux, the branching patterns of the insert must be avoided, in case the appropriate revisions in the architecture (width, location and cross section area) of the simple branchless patterns are considered. An analytical solution for predicting the peak temperatures in the chip is also addressed. It is demonstrated that under the same volume fraction and thermal conductivity of the cooling insert, the peak temperature is reduced to 2.9°C, which is 94% below the lowest temperature existed in the archival literature, which was around 50°C.