In this study, three computational approaches for the optimization of a thermal conduction problem are critically compared. These include a Direct Method (DM), a Genetic Algorithm (GA), and a Pattern Search (PS) technique. The optimization aims to minimize the maximum temperature of a hot medium (a medium with uniform heat generation) using a constant amount of high conductivity materials (playing the role of fixed factor constraining the considered problem). The principal goal of this paper is to determine the most efficient and fastest option among the considered ones. It is shown that the examined three methods approximately lead to the same result in terms of maximum temperature. However, when the number of optimization variables is low, the DM is the fastest one. An increment in the complexity of the design and the number of degrees of freedom (DOF) can make the DM impractical. Results also show that the PS algorithm becomes faster than the GA as the number of variables for the optimization rises.