This work presents a methodology for coupling two open-source modelling frameworks in a highly parallel fashion across multiple length scales to solve an electrical current and heat transport problem for commercial cylindrical lithium-ion batteries. The global current and heat transfer problems are formulated as resistor networks and solved using a finite difference method on a network extracted from an X-ray tomogram of an MJ1 18650 battery. The electrochemistry governing the heat generation is solved at the local level using a physically parameterized model. Electrochemical models are solved for different regions of a spirally wound cylindrical cell in parallel, coupled via charge conservation at the current collectors in a 'battery of batteries' fashion, similar to the concept of modelling a pack. Thermal connections between layers in the spiral winding are established and heat transport is solved globally in a two-dimensional fashion, allowing for the subsequent extension to three dimensions. Great heterogeneity in local current density is predicted by the model which is also found to have some temperature dependence with ramifications for battery degradation.