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As automotive emissions become more stringent, accurate control of three-way catalyst temperature is increasingly important for maintaining high levels of conversion efficiency as well as preventing damage to the catalyst. A real-time catalyst temperature model provides critical information to the engine control system. In order to improve emissions and ensure regulatory compliance over a wide range of speed-load conditions, it is desirable to use modelled catalyst temperature as the primary input to catalyst efficiency control strategies. This requirement creates a challenge for traditional empirical models designed for component protection at high speed-load conditions. Simulation results show that a physics aligned model can estimate temperature in all operating conditions, including: cold-start, extended idle, engine shutdown, stop-start events, deceleration fuel shut-off, as well as traditional high load and part load points.