This paper outlines measurements made at the National Research Council Canada (NRC) of the thermodynamic melting temperatures of Co–C, Pt–C and Re–C fixed points that have been part of the high-temperature fixed-point research plan of Working Group 5 of the Consultative Committee for Thermometry (CCT-WG5) to assign melting temperatures to those fixed points. This document will outline the equipment used, describe the scheme used to calibrate a pyrometer with traceability to a cryogenic electrical substitution radiometer, and detail the method of measuring the fixed points. It will then report the uncertainties in the measurements and the results. A brief description of the improvements that we plan to implement to the scheme to reduce the uncertainties for future measurements will be given. The thermodynamic temperatures determined for the three fixed points are: 1597.776 K with an expanded uncertainty of 0.36 K, 2011.390 K with an expanded uncertainty of 0.55 K, and 2748.056 K with an expanded uncertainty of 0.95 K, for the Co–C, Pt–C and Re–C fixed points, respectively (all expanded uncertainties assume a 95% confidence interval and a Gaussian distribution).