This paper presents a complete modelling of engine in-cylinder thermodynamics and exhaust heat transfer at engine cold start. The emphasis of the research was both on the effect of high values of ignition retard (HVIR) on the thermodynamic cycles of the engine and on the exhaust heat transfer for improved cold-start catalysts lightoff, and on the predictive capability of the model. Under extreme spark timing retard conditions, the Wiebe function describing the combustion rate of a fuel-air mixture was modified. An empirical correlation for cylinder pressure variation during the mass blowdown process, which occurs between the open exhaust valve and bottom dead centre, was included to enhance the predictive capability of the model. The complicated mass blowdown process across the exhaust valves was simplified by two processes: (i) isentropic expansion from the cylinder pressure to the constant exhaust manifold pressure, and (ii) constant pressure throttling that gives rise to increased exhaust gas temperature due to the recovery of kinetic energy. In the exhaust system, which includes a manifold, a pipe and a catalytic converter, a complete modelling of heat conduction, convection and radiation was performed. The thermal inertia of the pipe wall and the catalytic converter's substrate was represented by the heat capacitor in a thermal circuit approximation. A brief description of numerical solutions for coupled hyperbolic and parabolic partial differential equations in the exhaust heat transfer model is also presented. Finally, the predictive capability of the model is validated satisfactorily with experimental results. The lightoff point of the catalytic converter at 25 mm away from the inlet face of the monolith under 28 degrees CA of HVIR implementation (about 35 s after engine cold-start) agreed well with the result obtained from a previous study based on the hydrocarbons conversion efficiency.