Based on Planck’s law, the surface temperature of an object can be determined by measurement of emitted radiation. The equation for monochromatic radiation thermometry within a finite solid-angle was deduced, and it was found that if the surface temperature and spectral emissivity can be solved at the same time, the specific radiation measurement conditions for multi-spectral thermometry should be generally met that the radiation measurement should be implemented within an infinitesimal solid-angle or within a finite solid-angle only for a perfect diffuser. When the directional spectral emissivity modeled by finite polynomial series is employed and proper mathematical transformation is used, a universal equation for monochromatic radiation thermometry is obtained. So the restrictions in radiation measurement can be got rid of, but spectral emissivity may not be solved simultaneously. Multi-solution problem was preliminarily investigated, and so a solution was put forward that the channel number should be more than the number of the variables to be solved and the nonlinear least squares method should be used.