This study constructs a simulation framework of a "thermodynamic mechanism–data-driven" dual-wheel drive. It proposes a heat flow feature adaptive mapping neural network (HFAM-NN) that integrates heat flow conservation constraints to achieve efficient prediction of the temperature field and heat flux density. The experiment uses granite, water, and C30 concrete as heat storage materials, and is verified by 14.6 GB of experimental data. The results show that HFAM-NN is superior to traditional algorithms in temperature prediction accuracy (MAE) and heat flux calculation accuracy (MRE), and has the best prediction effect on water (MAE = 0.28∘C, MRE = 1.8%). The calculation efficiency is about six times higher than that of the finite element method (single working condition time is reduced from 270–45 minutes). This framework provides quantitative tools for the structural optimization of sensible heat storage systems and promotes the engineering application of cost-effective thermal energy storage technology.