Doped GeSbTe (GST)-based phase change materials are of growing interest due to their ability to enable high-temperature data retention for embedded memory applications. This functionality is achieved through Ge enrichment and addition of dopants such as N and C in stoichiometries such as GST-225, which improve the crystallization temperature and thermal phase stability. In this study, we examine the effect of these dopants on thermal conductivity using Raman thermometry. We report the temperature-dependent thermal conductivity of the amorphous and crystalline phases of Ge-rich GeSbTe (GGST) and Ge-rich GeSbTe N-doped (GGSTN) thin films. The results reveal a surprising temperature dependence of the thermal conductivity of the crystalline phase of GGST and GGSTN, a phenomenon not typically observed for GST-based materials. Additionally, enrichment of Ge and subsequent N-doping result in reduced thermal conductivity, which can benefit the power consumption of phase change memories. From a characterization perspective, Raman thermometry has been developed as a technique for simultaneous structural and thermal characterization of GST-based materials.