We report on the study of the temperature dependence of the response of a BSO crystal based polarimetric current sensor with spectral interrogation. Two possible interrogation schemes are discussed. The spectral dependence of the optical rotation along the crystal caused by temperature and current changes has been investigated and approximate dependences for the sensitivities to current SI and temperature ST have been derived. A mixed term in the response with spectral interrogation has been revealed, the elimination of which is done by tracking wavelength shifts of two distinct extrema in the polarimetric response. A temperature independent second degree equation for the current changes as a function of the spectral shifts has been derived and tested.