The flame is very hard to keep steadily symmetrical for a wide flammability limit under some extreme combustion conditions (such as large heat loss and fuel of low caloric value). Recently, we manufacture a mesoscale combustor with a plate flame holder and preheating channels, which could take the advantage of the flow recirculation and heat recirculation effects. The experimental results show that this special configuration performs excellent in flame-anchoring, and the flame can remain steadily symmetrical at very low equivalence ratio in the normal environment. In order to provide theoretical basis to optimize this combustor, the three-dimensional numerical simulation is used to study the thermal performances of solid walls on unburned fuel mixture quantitatively. The results indicate that the combustor wall does not always have preheating effects on the unburned mixture. Some walls or some parts of walls have the negative effect of heat loss. Furthermore, some interesting boundary shapes of the preheating areas or heat loss areas are found. It is deduced that the thermal performances of combustor walls mainly depend on the side with higher temperature. In addition, the preheating area decreases with an increasing flame height, so a lower flame height is probably beneficial for preheating.