This paper proposed a single-fluid Single Relaxation Time (SRT) lattice Boltzmann model, specifically designed to investigate the natural convection properties of Latent Functionally Thermal Fluid (LFTF). The study examines the effects of both constant and sinusoidal heat sources applied to the boundary walls. Additionally, a Back Propagation (BP) neural network model is utilized to predict the local Nusselt number at the wall. The results reveal that optimal heat transfer efficiency is attained when the phase transition temperatures are within the range of 0.3 to 0.7. It is also observed that the heat transfer effectiveness at the sinusoidally heated wall is directly proportional to the wall temperature. Moreover, for a certain phase transition temperature, a decrease in the Stefan number could make an increase in the latent heat associated with phase change, significantly boosts heat transfer within the confines of a square cavity. The BP neural network’s predictions are found to be highly reliable, with an error margin of approximately 5% when compared to the simulation results.