•Cold plate cooling of prismatic Li-ion battery under 5C discharging is modeled.•Temperature patterns on Li-ion battery with cold plate cooling are discussed.•Thermal responses of Li-ion battery under external shorting are simulated.•3D thermal modeling of 50 V Li-ion battery pack with 14 20 Ah cells is performed.•Multi-scale multi-domain modeling is demonstrated for large Li-ion battery pack. In this work, three-dimensional (3D) thermal modeling of a single Li-ion battery cell and a 50 V Li-ion battery pack composed of 14 prismatic batteries is performed. Equivalent circuit model is used for subscale electrochemical modeling. The heat generated by electrical resistance and electrochemistry reactions is then solved in the cell domain which resolves the heat transfer in battery and battery pack. The modeling provides highly resolved temporal 3D insight into thermal and battery dynamics under fast discharging and abusive condition. It is found that with low coolant velocity, the cell temperature easily exceeds 40 °C, and temperature non-uniformity exceeds the limit value of 5 °C under 5C discharging condition; and under external shorting condition, temperature rises fast and reaches the 80 °C point quickly which can further trigger thermal runaway. On the other hand, with adequate coolant flow rate, the cell temperature and temperature gradients are effectively limited to tolerable level under both 5C discharging and external shorting conditions. Thus, coolant rate needs to be carefully designed to prevent high temperature and localized high temperature spot in Li-ion battery. The modeling method used in this study can be applied to general Li-ion battery and Li-ion battery pack designing.