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A linear detector of thermal neutrons, developed at the Laboratory for High Energies (Joint Institute for Nuclear Research), is used in the polarized-neutron spectrometer of the aAe-2 reactor (JINR). The data are acquired in the regime of frame-by-frame survey to select neutrons with a wavelength λ = 1—12 A by the time of flight. The neutron-detection efficiency is ~70% for a wavelength of 2 A. The detector exhibits a low sensitivity to γ -rays, a dif- ferential nonlinearity of ~1.5%, and a spatial resolution of ~1.5 mm at counting rates of ~10 5 events/s.