Lithium-ion battery packs have become a dominant technology for automotive and grid energy storage due to their high energy density and relatively low cost. In these applications, a battery pack consists of many individual cells connected in series and parallel to meet the required energy and power demands of the system. Parallel connected battery modules can exhibit complex and unexpected behaviors due to the dynamics of current and temperature imbalances in the module, which are largely caused by cell-to-cell variability. As a module of parallel cells ages, current and temperature imbalances can accelerate the degradation of the module or cause individual cell failures. While standard battery management systems are able to monitor and balance series connected cells, sensor cost and space constraints prevent the BMS from monitoring single cells within parallel connected configurations. For this reason, thermal failures in a parallel module are liable to go undetected by the BMS. It is therefore important to understand the dynamics of parallel connected cells, and to define the parameter variability which can cause detrimental non-uniform heat generation in the system. To accomplish this, we have performed experiments to measure current and temperature dynamics during cycling of a parallel connected module. We have subsequently constructed an empirical model consisting of a temperature dependent equivalent circuit model for each cell to describe electrical dynamics, and a thermal circuit to describe temperature dynamics, and fit the model to experimental data. Finally, a sensitivity analysis has been performed for each model parameter to determine which kinds of cell-to-cell variability result in thermal gradients that are detrimental to the lifetime and safety of the battery pack.