True surface temperatures can be determined by measurements of radiation emitted by the object. The non-spectral parameter in the radiation measurement equation is the function of the relative position between the target and the lens, so calibration of space position is necessary for temperature measurement, when emissivity and temperature are measured simultaneously. In the present paper, the non-spectral parameter was included into the undetermined coefficients of emissivity modeled by finite series, which will not affect the solution of true surface temperature. Therefore, radiation thermometry can be accomplished without calibration of space position and normalization of measurement data. And not the true spectral emissivity but the trend of it can be measured. Two special examples were investigated, respectively. The results indicate that when the effective wavelength of each channel is different, multi-wavelength radiation thermometry equations have the unique solution, while the number of the multiband ones may be zero, one, two or even three.