The fine control of endpoint temperatures of the dome and exhaust gas is the key to improving the heat storage efficiency and capacity of the pebble stove combustion process. However, owing to nonlinearity, time delay, uncertain endpoint time, and strong coupling issues of the combustion process, it is difficult to achieve the desired dome and exhaust gas endpoint temperatures, simultaneously. Therefore, a two-stage (fast heating stage and heat storage stage) control system for the endpoint temperature is developed for the combustion process of the pebble stove. According to the heat transfer theory and the principle of conservation of heat, a transient heat transfer model between the flue gas and the regenerator is developed for the combustion process of the pebble stove. Based on the transient heat transfer model, prediction models of the dome and exhaust gas endpoint temperatures are obtained by a finite-difference method. Moreover, to solve the strong coupling between the dome temperature in the fast heating period and the exhaust gas temperature in the thermal storage period, a two-stage intelligent proportion-integral-derivative decoupling control algorithm is developed based on a self-refreshing recurrent neural network to realize the decoupling control of the dome and exhaust gas endpoint temperatures. The performance of the developed system is demonstrated with simulation and industrial experiments. The results show that compared to the conventional control system, the developed system effectively shortens the adjusting time of the dome endpoint temperature by 13 min with a reduced temperature fluctuation from +/- 14 degrees C to +/- 4 degrees C and increases the exhaust gas endpoint temperature from 328.3 degrees C to 348.0 degrees C. The enhanced temperature control performance demonstrates the validity of the established system.