Radiation thermometry techniques have been developed from monochrome thermometry for single-point temperature measurement to multi-spectral thermometry for 2D or 3D temperature field measurement in the past few years with the development of radiation measurement sensors, but it is difficult to overcome the temperature deter error resulting from the modeling of emissivity. Determining emissivity behaviors is difficult and important for decreasing temperature errors and a general method is required to avoid the influence of emissivity behaviors. Dual-wavelength thermometry techniques have been developed to determine the temperature on a gray-body surface, and a series of compensation algorithms and wavelength choosing algorithms have been proposed to decrease the temperature error in dual-wavelength thermometry but they still have been affected dramatically by emissivity behaviors. Sometimes the error of dual-wavelength thermometry using the ratio method is greater than that of monochrome thermometry. Multi-wavelength thermometry has been widely used, but the number of measurement channels and emissivity behaviors still have important influences on temperature errors. The direct emissivity constraint algorithm and the emissivity constraint algorithm using a relaxing factor for radiation thermometry have been developed in this paper to determine the true temperature approximately. There is equivalence between the two algorithms as the emissivity constraint is the same. The emissivity constraint algorithm using a relaxing factor utilizes the least square algorithm instead of the ratio method to determine the true temperature. The error equation of the radiation thermometry algorithm with emissivity constraint using a relaxing factor has been deduced. It can be found that decreasing the value of λT can decrease the relative error of temperature as the signal-to noise ratio for each channel is big enough to keep accurate signals. Emissivity behaviors have an important influence on temperature errors, and the obvious emissivity variation with wavelength within the constraint interval can make temperature errors decrease. The direct emissivity constraint algorithm shows that increasing the number of channels may decrease temperature errors. It is obvious from the two methods that decreasing the length of the shrunk range of emissivity can decrease temperature errors dramatically.