This study emphasizes the aspects of heat transfer and transient thermal distribution through a rectangular fin profile when a stretching or shrinking mechanism is mounted on the surface of the fin. Furthermore, the effects of radiation, internal heat generation, and convection are all considered when developing the corresponding fin problem. The simulated time-dependent heat transfer equation is a partial differential equation that can be represented by dimensionless arrangement using appropriate nondimensional terms. The nonlinear dimensionless problem concerning the stretching/shrinking of a fin is numerically solved using the finite difference method (FDM), and the Levenberg–Marquardt method of backpropagation artificial neural network (LMM-BANN) has been used in this investigation. By varying the stretching/shrinking parameter, a set of data for the presented artificial neural network (ANN) is produced to discuss stretching and shrinking scenarios. The testing, training, and validation procedure of LMM-BANN, as well as correlation for verification of the validity of the proposed approach, establish the approximate solution to stretching/shrinking scenarios. The suggested model LMM-BANN is then validated using regression interpretation, mean square error, and histogram explorations. The ANN results and the procured numerical values agree well with the current numerical results.