Phosphor-converted laser light sources have higher optical power densities than traditional lighting methods, which can translate to higher efficiency in many applications. Fluency Lighting Technologies has developed a composite phosphor conversion platform that consists of luminescent phosphors suspended within a transparent matrix. Thermodynamics is essential to the performance of the platform since phosphors lose up to half of their optical capacity at temperatures above 250 C. We studied how the heat generated during conversion is diffused through the material and how the structure of the composite impacts heat transfer. We further examined how contact-resistances, air gaps, and similar imperfections dictate the conductivity and diffusivity of the material. Due to the microscopic size and the complex composition of the phosphor converter, empirical measurements are challenging and limited in scope. Instead, we used Computational Fluid Dynamics simulations through the SolidWorks flow simulation package to examine the thermal properties of the converter. The simulations informed us of the local heat flux densities and the temperature gradients in the converter. This information was then processed to approximate an effective thermal conductivity for the composite. The results of this project will be used to review the design and the manufacturing process of the phosphor converter with a better understanding of its thermal characteristics.