Four independent radiation temperature scales approximating the ITS-90 at 900 nm, 950 nm and 1.6 µm have been realized from the indium point (429.7485 K) to the copper point (1357.77 K) which were used to derive by extrapolation the transition temperature T90(Co–C) of the cobalt–carbon eutectic fixed point. An INRIM cell was investigated and an average value T90(Co–C) = 1597.20 K was found with the four values lying within 0.25 K. Alternatively, thermodynamic approximated scales were realized by assigning to the fixed points the best presently available thermodynamic values and deriving T(Co–C). An average value of 1597.27 K was found (four values lying within 0.25 K). The standard uncertainties associated with T90(Co–C) and T(Co–C) were 0.16 K and 0.17 K, respectively. INRIM determinations are compatible with recent thermodynamic determinations on three different cells (values lying between 1597.11 K and 1597.25 K) and with the result of a comparison on the same cell by an absolute radiation thermometer and an irradiance measurement with filter radiometers which give values of 1597.11 K and 1597.43 K, respectively (Anhalt et al 2006 Metrologia 43 S78–83). The INRIM approach allows the determination of both ITS-90 and thermodynamic temperature of a fixed point in a simple way and can provide valuable support to absolute radiometric methods in defining the transition temperature of new high-temperature fixed points.