Unknown and varying emissivity is still one of the most important and the most difficult problems when radiation thermometers are applied to temperature measurement of heated sheet in steel-making processes. In previous reports, the authors proposed a new technique for emissivity-free temperature measurement by using spectral information of thermal radiation from targets and applying principal component analysis in order to overcome the problem of unknown and varying emissivity. More specifically, this is a passive method in which the principal component used for temperature measurement is experimentally determined in advance, and temperature is determined from the score (i.e. coefficient) of the principal component included in the measured spectrum of targets. This paper reviews the mathematical formulation of the concept and describes its application to a steel-making process to confirm the effectiveness of the technique.