The list of reacting flows in porous media applications is quite long, including porous media combustion, syngas production, and fuel cells. Porous media combustion is recognized as a cutting-edge combustion technique for increasing flammability. In this process, heat is transferred from the exothermic reaction zone to the incoming reactants through porous media. This role of porous media distinguishes reacting flows in porous media from free combustion processes. Local heat transfer, such as solid conduction, solid–solid radiation, and solid–gas convection, as well as the response behavior, are affected by the topology of the porous material. Theoretical studies indicate that continuously graded porous materials can significantly enhance the performance benefits of heat transfer. However, topology design is challenging for smooth graded porous media, and thus investigations of combustion within graded porous media are still required. In this study, we constructed a porous structure of type W/P/D/G (porosity ε = 0.3–0.5, hydraulic diameter dh = 1.33–3.86 mm) using a triply periodic minimal surface (TPMS), and a computational model of the combustion reaction in porous media was established to compare the range of flame stability within different pore types. In addition, topology gradation was achieved via TPMS to modulate the heat transfer to ensure the dependable functioning of premixed flames and improved heat recirculation. Heat transfer in the graded TPMS-based porous structure was analyzed numerically. The conclusions obtained from this study can effectively address the aforementioned challenges related to porous media burner design.