This study presents an approximation for determining an optimized thickness of a concentric heated rectangular plate and derives an analytical solution for spreading resistance of a spreader having orthotropic conductivities. The solution for the orthotropic plate is obtained by separation of variables, and the optimized thickness is determined by taking the derivative of the thermal resistance with respect to the spreader thickness. According to the calculated results, an enhanced in-plane spreading effect can reduce the spreading resistance. The spreading resistance dominates the overall resistance of thin plates, whereas the one-dimensional conduction resistance becomes important for thick plates. However, the predicted optimized thickness from the approximation shows a disparity from the analytical results, while the aspect ratio between a spreader and heat source is less than 0.2. Even so, the thermal resistance corresponding to the predicted thickness is still in good agreement with the analytical solution. The proposed approximation will be useful for practical thermal design of heat sinks by predetermining the spreader thickness.