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In the catalytic converter, the thermal conductivity of the insulation material (intumescent mat) placed between the ceramic catalyst and the metal shell is strongly dependent on the temperature, resulting in the solving of non-linear heat conduction equations. In this paper, the analytic solution for the steady heat flow in a cylinder with temperature dependent conductivity is given. Using this analytic solution for the mat and including convection and radiation at the converter skin, an analytical expression for calculating converter skin temperature is obtained. This expression can be easily incorporated in a Fortran code to calculate the temperatures.