The high-temperature extension of the fixed-point technique for primary calibration of precision infrared (IR) thermometers was investigated both through mathematical simulations and laboratory investigations. Simulations were performed with Co–C (1,324°C) and Pd–C (1, 492°C) eutectic fixed points, and a precision IR thermometer was calibrated from the In point (156.5985°C) up to the Co–C point. Mathematical simulations suggested the possibility of directly deriving the transition temperature of the Co–C and Pd–C points by extrapolating the calibration derived from fixed-point measurements from In to the Cu point. Both temperatures, as a result of the low uncertainty associated with the In–Cu calibration and the high number of fixed points involved in the calibration process, can be derived with an uncertainty of 0.11°C for Co–C and 0.18°C for Pd–C. A transition temperature of 1,324.3°C for Co–C was determined from the experimental verification, a value higher than, but compatible with, the one proposed by the thermometry community for inclusion as a secondary reference point for ITS-90 dissemination, i.e., 1,324.0°C.