The use of an extended surface (fin) is one of the important ways to heat transfer from the engines and all kinds of electrical transformers. Therefore, it is so important to study and obtain the best conditions of operation to get the best performance per unit cost. This research presents an analytical study to obtain the temperature distribution through a finned surface. Two new suggested techniques based on the finite element method to obtain the optimum design of finned surface subjected to logarithmic temperature profile were presented. The suggested techniques are based mainly on the temperature difference along fins domain in the longitudinal and transverse directions. A simple apparatus of rectangular fins is studied to obtain the optimum design related to its dimensions. The finite element technique (Ansys 9) is used to simulate and solve the governing differential equations. The problem was considered under free convection mode. It was noted that the suggested optimized criterion give an excellent results as compared with the original fin shape. The temperature response plays an important rule in the selection of suitable optimized criteria. It is so important to present that the profile of the optimized fin length is largely depends on the temperature profile that firstly applied on the fins surface.