A numerical analysis has been conducted to examine the heat transfer characteristics of a finned heat pipe based on thermal resistance networks. The present numerical analysis also reports the enhancement of heat transport of heat pipe using the fins. The key simulation parameters considered were three types of fins with circular, square, and hexagonal shapes, the fin length in the range from 19.05mm to 38.1mm, the number of fins in the range from 5 to 20, and the fin thickness in the range from 0.25mm to 1mm. The heat transfer rate shoots up by 62.58% in the case of finned heat pipe when compared with the baseline model with respect to the variation in the simulation parameters. An artificial neural network, which is one of the machine learning methods, was used to predict the heat transfer performance obtained from thermal resistance analysis of the finned heat pipe. The optimized ANN model could predict the heat transfer performance of the finned heat pipe with reasonable accuracy. In addition, the heat transfer rate of the finned heat pipe could be predicted accurately from extrapolated and interpolated data using the optimized ANN model.