The inverse computational fluid dynamics simulation combined with experimental temperature measurements is applied to investigate the three-dimensional natural convection of an innovative plate heat exchanger in a hot box. This natural convection conjugate heat transfer separated by all insulating walls of the hot box is solved by couping. The upper low-temperature duct is located between the lower high-temperature duct and the top wall of the hot box. If the root mean square error between the obtained numerical results of the air temperature and the experimental data at the selected measurement locations is the smallest among all flow models, then the appropriate flow model and wall function can be predicted. Furthermore, more accurate natural convection heat transfer characteristics and the heat transfer rate applied to the two ducts can be determined. An important finding is that the realizable k-ε model combined with the standard wall function and the zero-equation model are suitable for problems with smaller and larger duct spacings, respectively. This means that the location of the two ducts may influence the selection of an appropriate flow model. In addition, increasing the number of grid points does not necessarily lead to more accurate results. An optimal total grid points can be obtained. The obtained heat transfer coefficients on the upper surfaces of the two ducts are also in good agreement with the existing correlation. This comparison further verifies that the present results and the selected flow model are accurate. Due to the blocking, buoyancy and heat dissipation effects of the two ducts, the formation of the main vortex, the velocity patterns and air temperature contours obtained by the two selected appropriate flow models are slightly different. The two gaps between the edges of the ducts and the side walls of the hot box can destroy the structure of natural circulation and improve the heat accumulation under the two ducts. The air flows slightly in the direction of the larger gap so that the velocity pattern and the temperature contour become asymmetric. As far as we know, these findings have not yet appeared in the public literature. Therefore, this study is novel and innovative.