Based on the principle of minimum volume, an optimum shape of spine is proposed at a given heat duty, base temperature, and fin length. Both the thermal conductivity and heat transfer coefficient are temperature dependent. In this study, a power-law type wall heat flux is employed. A uniform temperature is assumed at the fin base whereas two kinds of boundary 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 fluids. Special cases of negligible heat transfer from fin tip and zero tip temperature are investigated. The temperature distributions and the profiles of the optimum fins are calculated for various single heat transfer modes. The results are presented in non-dimensionalized form for the convenience of parametric study and design analysis.