Involved in all possible types of heat transfer, the thermal characteristics of a single fin with and without heat transfer at its tip is studied. The heat transfer coefficient is assumed to vary with a power-law-type formula. Based on the value of the exponent, the problem is categorized into three regimes. The temperature distribution and heat transfer rate are given in implicit forms and solved exactly. No solution is found when the fin parameter exceeds a specific value for a negative exponent. Besides. two solutions are detected when the fin parameter is smaller than this value, which is related to the thermal instability. Results from analysis are compared with experimental data.