This paper briefly describes the characteristics of all-solid-state lithium-ion battery and the significance of investigation on the internal thermal transport. The related experimental and theoretical works on the thermal transport properties of cathode materials, anode materials, solid-state electrolytes, and electrode-electrolyte interfaces are introduced and summarized. In view of the unclear mechanism of the influence of lithium insertion and extraction process on the thermal conductivity of electrode materials, the challenge of solid-state amorphization to the research of thermal transport, and the limitation of models and methods in heat transport across the interface, we systematically sort out the important scientific issues of thermal transport in all-solid-state lithium-ion battery.