Third-generation photovoltaic materials, including metal halide perovskites (MHPs), colloidal quantum dots (QDs), copper zinc tin sulfide (CZTS), and organic semiconductors, among others, have become attractive in the past two decades. Unlike their first- and second-generation counterparts, these advanced materials boast properties beyond mere photovoltaic performance, such as mechanical flexibility, light weight, and cost-effectiveness. Meanwhile, these materials possess more intricate crystalline structures that aid in understanding and predicting their transport properties. In particular, the distinctive phonon dispersions in MHPs, the layered architecture in quasi-two-dimensional (2D) perovskites, the strong quantum confinement in QDs, and the complex crystal structures interspersed with abundant disorders in quaternary CZTS result in unique and sometimes anomalous thermal transport behaviors. Concurrently, the criticality of thermal management in applications such as photovoltaics, thermoelectrics, light emitting diodes, and photodetection devices has received increased recognition, considering that many of these third-generation photovoltaic materials are not good thermal conductors. Effective thermal management necessitates precise measurement, advanced modeling, and a profound understanding and interpretation of thermal transport properties in these novel materials. In this review, we provide a comprehensive summary of various techniques for measuring thermal transport properties of these materials and discuss the ultralow thermal conductivities of three-dimensional (3D) MHPs, superlattice-like thermal transport in 2D perovskites, and novel thermal transport characteristics inherent in QDs and CZTS. By collecting and comparing the literature-reported results, we offer a thorough discussion on the thermal transport phenomenon in these materials. The collective understanding from the literature in this area, as reviewed in this article, can provide guidance for improving thermal management across a wide spectrum of applications extending beyond photovoltaics.