A recent mathematical technique of homotopy perturbation method (HPM) for solving nonlinear differential equations has been applied in this paper for the analysis of steady-state heat transfer in an annular fin with temperature-dependent thermal conductivity and with the variation of thermogeometric fin parameters. Excellent benchmark agreement indicates that this method is a very simple but powerful technique and practical for solving nonlinear heat transfer equations and does not require large memory space that arises out of discretization of equations in numerical computations, particularly for multidimensional problems. Three conditions of heat transfer, namely, convection, radiation, and combined convection and radiation, are considered. Dimensionless parameters pertinent to design optimization are identified and their effects on fin heat transfer and efficiency are studied. Results indicate that the heat dissipation under combined mode from the fin surface is a convection-dominant phenomenon. However, it is also found that, at relatively high base temperature, radiation heat transfer becomes comparable to pure convection. It is worth noting that, for pure radiation condition, the dimensionless parameter of aspect ratio (AR) of a fin is a more desirable controlling parameter compared to other parameters in augmenting heat transfer rate without much compromise on fin efficiency.