The degradation rate of Li-ion batteries and therefore their useful life depends on many parameters, including temperature, charge/discharge rates, the chemistry and microstructure of electrodes. The importance of understanding these mechanisms explains the large interest in developing predictive electrochemical ageing models accounting for the known deterioration mechanisms, mainly related to SEI layer formation and Li-plating. Usually, these ageing models are developed and applied at cell level assuming perfect uniformity in all dimensions apart from the through-plane direction. In this work, we extend the model to all dimensions within the cell to account for intra-cell non-uniformities in terms of local temperature and current. However, the temperature distribution of a cell within a battery pack depends on the interaction with its environment, which typically involves active cooling via an external fluid circulation within a channel network. Therefore, to obtain the temperature distribution within the cell, it is necessary to solve for the 3-dimensional field in the pack. In fact, this solution needs to account for the heat source terms generated in the cells during operation, especially during fast-charging, where heat release becomes critical. In this work, we solve the multi-dimensional thermal and electrochemical problem of battery operation during fast-charging including a detailed electro-chemical ageing model which predicts the formation of Li-plating and SEI formation. The thermal and electrochemical models are calibrated via in-house experiments. The simulation is performed using a commercial software. The results illustrate that battery degradation can have substantial intra-cell and intra-pack non-uniformities due to the non-uniform heat dissipation during fast-charging. The modeling approach presented here can be further used as a tool to predict the battery lifetime and optimize its design and cooling system parameters.