In battery packs with cells in parallel, the inter-cell connection resistances can cause unequal loads due to non-uniform interconnect overpotentials and consequentially lead to non-uniform heating. This article explores how load imbalances are generated in automotive applications, by describing a battery pack with finite interconnect resistances. Each cell inside the pack is represented by a pseudo 2D electrochemical model coupled with a lumped thermal model. Increasing the number of cells in parallel results in a linear increase in load non-uniformity, whilst increasing the ratio of interconnect to battery impedance results in a logarithmic increase in load non-uniformity, with cells closest to the load points experiencing the largest currents. Therefore, interconnect resistances of the order of mΩ can have a significant detrimental impact. Under steady state discharge the cell impedance changes until the loads balance. This process, however, can take hundreds of seconds and therefore may never happen under dynamic load cycles. Cycling within a narrow state-of-charge range and pulse loading are shown to be the most detrimental situations. Upon load removal, re-balancing can occur causing further heating. Simulation of a 12P7S pack under a real world load cycle shows that these effects could cause localised thermal runaway.