Multispectral radiation thermometry is an effective method for measuring the true temperature of objects using radiation. However, traditional hardware based spectral splitting methods cannot obtain the brightness temperature across multiple spectra for true temperature inversion due to the weak radiative energy and low signal-to-noise ratio of medium and low temperature targets. To address this issue, this paper proposed a measurement method for obtaining brightness temperatures across multiple spectra based on computational spectral splitting. First, a compressed sensing and reconstruction method for spectral radiance signals is proposed based on a broadband filter encoding structure. Second, a theoretical basis for the selection of dictionary learning samples in multispectral brightness temperature measurement is provided. Then, an overcomplete dictionary is designed using the K-SVD optimization learning algorithm to sparsely represent spectral radiance signals, and the OMP greedy algorithm is used to reconstruct multispectral radiance signals. Finally, the brightness temperature calculation under the reconstructed spectra is achieved based on radiation thermometry theory. Experimental results indicate that the proposed method effectively measures the multispectral brightness temperature of medium and low temperature targets for different materials, with a measurement error of no more than 0.9%.