High-throughput computational and experimental design of materials aided by machine learning have become an increasingly important field in material science. This area of research has emerged in leaps and bounds in the thermal sciences, in part due to the advances in computational and experimental methods in obtaining thermal properties of materials. In this paper, we provide a current overview of some of the recent work and highlight the challenges and opportunities that are ahead of us in this field. In particular, we focus on the use of machine learning and high-throughput methods for screening of thermal conductivity for compounds, composites and alloys as well as interfacial thermal conductance. These new tools have brought about a feedback mechanism for understanding new correlations and identifying new descriptors, speeding up the discovery of novel thermal functional materials.