High-temperature thermal transport is fundamentally important for a multitude of energy conversion and storage processes, such as power generation (e.g., gas turbines), thermochemical, solar-thermal, thermophotovoltaic, thermoelectric, and thermal energy storage. Heat transfer physics at high temperature is also markedly different from its counterpart at room- and low- temperatures, including higher degree of anharmonity of lattice dynamics resulting in stronger phonon-phonon scattering and the more prominent or even dominant role of radiation heat transfer. On the other hand, high temperature poses tremendous challenges on the materials, especially on their thermal and chemical stability. We have been working on several fronts related to high temperature thermal transport materials and physics over the past few years, including the development of high-temperature materials and devices for engineering applications in solar energy harvesting, thermal insulation, thermal storage, heat exchangers, selective emitters, etc., as well as basic studies of conduction-radiation coupled phenomena in nanostructures at high temperature. In this talk, I will specifically present two recent examples of our work in this area. First, we experimentally probed the more prominent role of surface phonon polariton (SPhP) in polar dielectric (e.g., SiO2) nanostructures and studied their contribution to radiation and conduction heat transfer from room to high temperature. We found that SPhP could be a significant energy carrier for heat conduction at high temperature. Second, we characterized and modeled thermal transport properties of moving granular media, which are being investigated as alternative high-temperature heat transfer and thermal energy storage medium (to replace molten salts). Due to the discrete nature of the granular media, we found that the particle-wall thermal resistance and the thermal conductivity in the bulk of the particle bed are both dependent on the flow state of the particles.