Parallel connected battery modules are a necessary component of large battery packs to increase the overall pack capacity. Unlike series connected cell systems, conventional parallel battery modules have a sparse sensing arrangement such that the battery management system (BMS) does not measure individual cell currents and temperatures. In this arrangement, single cell failures and current and temperature gradients are liable to go undetected by the BMS. As a result of this, it is important to understand the current and temperature dynamics within a parallel connected cell module, so that packs can be designed to mitigate these failures, and BMS diagnostic tools can overcome the aforementioned sensing challenges. In this work, we combine parallel module cycling experiments with a nonlinear model of the system to investigate which parameters contribute the most to thermal gradients. Cycles were performed on a 1S4P module of prismatic LFP cells, recording individual cell currents and temperatures, while adjusting the contact resistance arrangement between each cycle to represent different failure and degradation scenarios. The module was discharged at 0.45C (504 A) to match the power capability and current draw of a 2-hour grid storage module in a large scale storage system. We then built an empirical model of parallel cells that consists of a temperature dependent equivalent circuit model (ECM), and a thermal circuit for each cell. The differential algebraic equation which describes the parallel coupling of the system is resolved using Schur decomposition in order to calculate the individual currents for each cell, so that total module current can be used as the model input, and cell surface temperatures are the outputs. Furthermore, we account for the Arrhenius behaviour of the charge transfer kinetics using a temperature dependent resistance in each cell ECM. The model was then fit to the experimental data from cycling to instil confidence that it accurately reproduces the behaviour of a true grid storage system. Finally, a Sobol sensitivity analysis has been completed to analyse which system parameters have the greatest effect on the thermal gradients. The sensitivity analysis shows that for prismatic LFP cells, the thermal gradient is primarily dependent on inconsistencies amongst contact resistance and internal cell resistance, although there are a myriad of possible parameter variation scenarios, and so capacity imbalances should also be kept to a minimum as shown by the Sobol Index.