Insight of thermal behaviour of lithium-ion batteries under various operating conditions is crucial for the development of battery management system (BMS). Although battery thermal behaviour has been studied by published models, the reported modelling normally addresses either normal operation or thermal runaway condition. A comprehensive electro-thermal model which can capture heat generation, voltage and current variation during the whole process from normal cycling to thermal runaway should be of benefit for BMS by evaluating critical factors influencing potential transition to thermal runaway and investigating the evolution process under different cooling and environment conditions. In this study, such a three-dimensional model has been developed within the frame of open source computational fluid dynamics (CFD) code OpenFOAM to study the electrical and thermal behaviour of lithium-ion batteries (LIBs). The equations governing the electric conduction are coupled with heat transfer and energy balance within the cell. Published and new laboratory data for LiNi0.33Co0.33Mn0.33O2/Li1.33T1.67O4 (LNCMO/LTO) cells from normal cycling to thermal runaway have been used to provide input parameters as well as model validation. The model has well captured the evolution process of a cell from normal cycling to abnormal behaviour until thermal runaway and achieved reasonably good agreement with the measurements. The validated model has then been used to conduct parametric studies of this particular type of LIB by evaluating the effects of discharging current rates, airflow quantities, ambient temperatures and thickness of airflow channel on the response of the cell. Faster function losses, earlier thermal runaway and higher extreme temperatures were found when cells were discharged under higher current rates. The airflow with specific velocity was found to provide effective mitigation against over-heating when the ambient temperature was below 370 K but less effective when the ambient temperature was higher than the critical value of 425 K. The thickness of airflow channel was also found to have critical influence on the cell tolerance to elevated temperatures. These parametric studies demonstrate that the model can be used to predict potential LIB transition to thermal runaway under various conditions and aid BMS.