The results of optimisation calculations presented in the article are related to longitudinally finned tubes of a heat pump evaporator operating under natural wind-induced flow of outdoor air conditions. The finned surface is characterised by an unusual, wavy fin shape. The article presents the methodology applied to seeking optimal geometric parameters of the finned tube in which thermal calculations were performed by modelling a mixed convection process on the finned surface using the finite volume method. In the case of maximising the heat flow with the minimum mass of the fins, the optimal solution was dominated by the minimum mass of the fins and thus geometric parameters correspond to the number of fins n = 6, fin height h = 0.065 and fin thickness s = 0.0015 m. Optimisation calculations made for maximum efficiency of the exchanger at constant mass indicated that the tube with ten fins (n = 10) with a height of h = 0.11 m and a thickness of s = 0.0018 m allowed maximum heat flow at the assumed mass of the fins in the exchanger tube model. The article proposes a simplified method of determining the optimal geometric parameters of the profile for any mass and maximum thermal efficiency.