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The causes of the fracturing of stone grills in barbecue ovens were analyzed using a coupled analysis model that combined combustion thermodynamics with heat conduction and the finite element method. The proportion of mixed air for combustion was simulated, and the stone grill plate temperature and thermal stress distribution were the two factors taken to enhance the design of stone grill plates. Moreover, thermal images were used to compare the performance of the original and the improved plates to quantify the improvements, and validate the accuracy of the simulations. The results showed that the temperature distribution was uniform across the stone grill plate. When comparing the simulation model and the actual experiment, the simulation model can generate an optimal design with fewer errors in a shorter period. The combustion tube is deemed to have considerable influence on the performance of the barbecue oven. The surface temperature distribution of the stone grill plate was improved by controlling the amount of fuel entering the combustion system and/or changing the material and shape of the stone grill. On the other hand, the analysis results of the improved stone grill plate in this study showed that we can correct the temperature difference and thermal stress difference caused by the opening of the upper cover of the oven. According to our study, the average thermal stress on the surface of the stone grill plate was effectively reduced by 45.3 MPa. The average temperature difference decreased by 91 °C. At the same time, by improving the intake position and method of the combustion tube, the air mass flow in the combustion tube increased by 12%, which effectively improved the combustion efficiency of the combustion tube. In particular, a more uniform distribution was achieved by decreasing the temperature of the mixed air entering the combustion tube, which in turn increased the flow rate and velocity of the air flowing through the top of the flame to the bottom surface of the stone grill plate. The strategies employed can prevent the thermal-stress-induced fracturing of stone grill plates and prolong their service life.