A triangular fin with variable fin base thickness and base height is analyzed and optimized for the fixed fin base height using a two-dimensional analytical method. At the middle of the fin length, the variation of the temperature along the fin height is listed. The influences of the fin length, base thickness and base height on the heat loss and fin efficiency are analyzed, The optimum heat loss, corresponding optimum efficiency and optimum fin length as a function of the fin base thickness are presented. The optimum heat loss and optimum fin tip length as a function of the convection characteristic number are represented.