A reduced-order model (rom) of mould heat transfer in the continuous casting of steel is presented and demonstrated for several commercial mould geometries. The rom relies on a physically-based solution of the one-dimensional heat-conduction equation. The up-front cost of the rom is a single three-dimensional finite-element calculation of a small representative portion of the exact mould geometry, which is used to calibrate the geometric parameters of the rom. Specifically, the rom exactly matches the average hot and cold surface temperatures of the mould as computed in the snapshot model. Other features of the rom, namely predictions of the cooling water temperature change and thermocouple temperatures, are derived in a manner consistent with the one-dimensional solution. Combined with models of solidification and mould-metal interfacial phenomena, this accurate and efficient modelling tool can be applied to enable deeper insight into many different aspects of heat transfer and related phenomena in the continuous casting process.