Multilayer capacitors (MLCs) represent promising electrocaloric (EC) cooling elements because they operate at low voltages, they possess large breakdown fields, they contain inner electrodes that facilitate heat transfer, and they exhibit a macroscopic volume of active EC material. However, almost ten years after they were first suggested as EC elements, the internal heat flow has not been well studied. In this paper, we use an infrared camera to investigate heat flow within representative MLCs of Pb(Mg,Nb)O3, and we achieve good agreement with the results of finite element modelling (FEM) by identifying for the inner electrodes an effective thermal conductivity that represents the limiting factor for heat flow. Increasing the inner electrode thickness by a factor of five would increase heat flow by a factor of 2.6. Our work therefore shows that FEM can play an important role in MLC design for EC applications.