Three-way catalytic converters used on spark ignition engines have performance and durability characteristics which are effected by the thermal environment in which these operate. The design of the exhaust system and the location of the catalyst unit are important in controlling the range of thermal states the catalyst is exposed to. A model of system thermal behaviour has been developed to support studies of these. The exhaust system is modelled as connected pipe and junction elements with lumped thermal capacities. Heat transfer correlations for quasi-steady and transient conditions have been investigated. The catalytic converter is treated as elemental slices in series. Exothermic heat release and heat exchange between the monolith, mat, and shell are described in the model. A similar description is applied to lean NOx trap units. Agreement between predictions and experimental data is good for streamwise temperature distributions throughout the system, and temporal variations under drive cycle conditions. The model is computationally efficient, and requires around 2 minutes of run-time on a Pentium PC computer to simulate system behaviour over an NEDC or FTP-75 drive cycle.