The profile of the least-weight longitudinal cooling fin is obtained considering temperature dependence of thermophysical properties. A power-law-type wall heat flux is assumed on the lateral and tip surfaces of the fin. Uniform temperature is imposed at the fin base, whereas two kinds of boundary conditions at the fin tip are considered. First, a specified heat transfer rate is prescribed at the free end. Second, the outer edge of the fin is also subject to a power-law-type surface heat flux and dissipates energy to the ambient fluid. Special cases of negligible heat transfer from the fin tip and zero tip temperature are investigated. The temperature distributions and profiles of the optimum fins are calculated for various single heat transfer modes. In addition, it is shown that the fin length plays an important role in the determination of the optimum fin with minimum volume.