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Heat is fundamental to power generation and many industrial processes, and is most useful at high temperatures because it can be converted more efficiently to other types of energy. However, efficient transportation, storage and conversion of heat at extreme temperatures (more than about 1,300 kelvin) is impractical for many applications. Liquid metals can be very effective media for transferring heat at high temperatures, but liquid-metal pumping has been limited by the corrosion of metal infrastructures. Here we demonstrate a ceramic, mechanical pump that can be used to continuously circulate liquid tin at temperatures of around 1,473-1,673 kelvin. Our approach to liquid-metal pumping is enabled by the use of ceramics for the mechanical and sealing components, but owing to the brittle nature of ceramics their use requires careful engineering. Our set-up enables effective heat transfer using a liquid at previously unattainable temperatures, and could be used for thermal storage and transport, electric power production, and chemical or materials processing.