Precise and accurate high temperature measurements are crucial for piloting material manufacturing processes more finely and obtaining the desired properties. These measurements are subjected to disturbances due to numerous measurement biases and experimental noises. In the context of this study, the metrological tool used for the measurements is the multi-spectral infrared thermography. The non-intrusive tool is coupled with minimization algorithms for the estimation of the surface temperature of opaque bodies. A major challenge for temperature estimation is the lack of knowledge of the optical properties of opaque materials and their evolution as a function of temperature, wavelength and time, which can deteriorate the accuracy of the estimation. To avoid this problem, a multi-spectral method has been developed to estimate simultaneously the spectral emissivity and temperature by using the analytical expression of the spectral emittance (Planck's law) with a spectral emissivity model based on finite element formulation using P1 elements. By using this method, the so-called "piecewise" functions are able to describe in high accuracy several types of emissivity variations by using continuous functions and derivatives. Theoretical and experimental estimations with metallic materials have shown that the multi-spectral method is able to estimate the surface temperature and the spectral emissivity with high precision and therefore reduce the systematic bias.