Inhomogeneity across individual battery modules, varying thermal loads, and cell-to-cell imbalances influence the battery pack performance characteristics. The cold plate that provides the cooling, delivers through multiple steps of thermal conduction and coolant fluid flow via multiple flow passages. Detailed thermal modeling of cold plates and battery packs with individual cells is reported in literature. However, they report within their own individual disciplines, namely electro-thermal or thermo-fluid and often with restrictive configurations. High-fidelity systems modeling of such multiple disciplines both together is not reported. A detailed system model developed has a cold plate with thermal conduction, coolant fluid flow, and electro-thermal battery pack. The battery pack has inherent cell-to-cell variations, and it exchanges heat dynamically with the cold plate. The discretized coolant flow passages vary in their configuration and geometry. The cold plate and individual cells battery pack are automatically generated into multidisciplinary, discretized components, equation-based, and acausal system models using Modelica language. We perform the systems modeling simulations with various configurations that compare multiple cold plate designs, bringing out the pattern of cooling with variation of temperature between individual cells and the effects of inherent cell-to-cell inhomogeneity.