Heat transfer can be drastically limited in non-uniform materials due to enhanced phonon scattering. The decrease of the thermal conductivity is related to the details of the microstructure. Understanding and modeling this relation would be useful in designing structures for applications such as efficient energy converters. We have examined mesoscopic structures consisting of two phases that differ in the thermal conductivity using the phonon Monte Carlo and Molecular Dynamics techniques. The results have been analyzed in terms of a thermal network model. Phenomenology has been developed extending existing Effective Medium Approximation models that interprets the MC results and provides physics insight. We have systematically explored the effects of the characteristic lengths and the dimensions of the nanoscale non-uniformity. These dependences are introduced as parameters in the phenomenological model. Transition from ballistic to diffusive transport signature in thermal transport is explicitly indicated. We discuss our results and we use the parametric modeling to provide generic conclusions.