The work described in this thesis concerns the continued development and application of a computational model to simulate the thermal behaviour of internal combustion engines. The model provides information on temperature and heat flow distributions within the engine structure, and on temperatures of oil, coolant and engine-out exhaust gas. Sub-models calculate friction levels, fuel flow rates and gas-side heat transfer, including the effects of exhaust gas recirculation (EGR), spark advance and turbocharging. The effects of auxiliary components such as a cabin heater, oil cooler, intercooler, supplementary heater and EGR cooler can also be simulated. Model developments are aligned towards improving the accessibility of the model and the scope of engine systems that can be simulated. Early versions of the model have been converted from 'C' into the current MATLAB/Simulink versions. The model structure and conversion process are described. New developments undertaken have focused on the external coolant circuit and include the modelling of the thermostat and radiator. A semi-empirical thermostat model is presented. A radiator model based on the effectiveness-NTU method is described. Simulations using the developed model, including the thermostat and radiator sub-models, investigate the effect of thermostat position on engine thermal behaviour. Positioning the thermostat on the inlet to the engine reduces thermal shock. Applications of the model to investigations of sensitivity and performance illustrate the accuracy of and confidence in model predictions. Assessments demonstrate that the model is relatively insensitive to variations of 100/0 in user inputs and is very sensitive to model assumptions if simulation conditions, implied in the model assumptions, are not matched to test conditions. A process for evaluating model performance is described. Evaluation exercises applied to three different engines demonstrate that values predicted by the model are to within 5 to 10% of experimental values. Investigations using the model of methods to improve warm-up times and fuel consumption prior to fully warm conditions show the benefits or otherwise of reduced thermal capacity, an oil cooler, a sump oil heater and an oil-exhaust gas heat exchanger. Each method is assessed over the New European Drive Cycle (NEDC) from a -10°C start. Of these methods, a combined reduction in coolant volume and engine structural mass is most beneficial for reducing coolant warm-up times. An oil-exhaust gas heat exchanger produces the greatest reduction in fuel consumption.