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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.