The numerical simulation of fluid flow through a complex geometry with heat transfer is of strong interest for many applications, such as oil-filled power transformers. A fundamental challenge here is that high resolution is necessary to resolve the fluid flow phenomena, but this makes simulation of the full geometry very expensive in terms of computational power. In this work, we develop a simulation methodology that combines a porous-medium approach for simulating some regions of the domain, coupled with fully resolved simulations in those regions which are deemed most interesting to study in detail. As one does not resolve flow features like thermal boundary layers in the regions modeled with the porous approach, the resolution in these parts can be orders of magnitude coarser. This multiscale approach is validated against the use of fully resolved simulations in the whole domain, as well as against analytical solutions to the extended Graetz problem. We then apply the approach to the study of oil flow and heat transfer in large electric power transformers and demonstrate a significant reduction in computational cost compared to a fully resolved approach.