We present an empirical PDE model for the description of the interplay between total current and heat flow in large-area organic LEDs, which can lead to unwanted spatial brightness in homogeneities. The model resolves the different layers in the OLED stack by taking their individual IV characteristics into account. In particular, the electrical conductivity features a field dependence to incorporate the non-Ohmic behavior of the organic materials and a temperature dependence via an Arrhenius law. We discuss the numerical scheme and present simulation results that confirm the experimentally observed S-shaped IV characteristics with regions of negative differential resistance, which cause the inhomogeneities.