The design and implementation of a sub-THz spectrometer for operations at temperatures down to 340 mK was demonstrated. A Martin-Puplett (MP) interferometer was coupled to a cryostat housing two independently controlled platforms cooled down with He-3 for operations under extreme conditions. A two-channel signal detection scheme was developed which was conveniently enabled by the optical layout of a MP interferometer. The results show that the two-channel detection minimized uncertainties in sub-THz measurements induced by relatively slow data acquisition.