At the engine restart, when the temperature of the catalytic converter is low, additional fuel consumption would be required to warm up the catalyst for controlling exhaust emission.The aim of this study is to find a thermally optimal way to reduce fuel consumption for the catalyst warm up at the engine restart, by improving the thermal retention of the catalytic converter in the cool down process after the previous trip.To make analysis of the thermal flow around the catalytic converter, a 2-D thermal flow model was constructed using the thermal network method. This model simulates the following processes: 1) heat conduction between the substrate and the stainless steel case, 2) heat convection between the stainless steel case and the ambient air, 3) heat convection between the substrate and the gas inside the substrate, 4) heat generation due to chemical reactions. The points to be especially noted are: a) in the cool down process, free convection of the gas inside the substrate was based on Darcy's law, b) in the engine operating condition, chemical phenomena and species mass balance in gas phase and catalyst surface was considered. The model was verified by comparing calculated results with experimental measurements.According to this thermal flow model, in the cool down process, heat from the substrate was mainly conducted through the stainless steel case, and dissipated to the ambient air. The effect of free convection of the gas inside the substrate was predicted to be small. Therefore, an effective way to improve the thermal retention of the catalytic converter was to interrupt the heat conduction between the substrate and the boundary surface to the ambient. In this paper, we propose an optimal way to improve the thermal retention of the catalytic converter while not to deteriorate its cooling performance at high load operation.