Thermal-vacuum environment adaptability is one of the key performances of space optical instru-ments, especially for hyper-spectral instrument, and spatial heterodyne spectrometer (SHS) should provide high spectral stability for the detection of atmosphere CO₂. Based on the research of the spatial heterodyne interfer-ence principle, simulation test in thermal-vacuum environment and quantitative analyses are carried out. The re-lationship among environment changes and the divergence half-angle of collimating lens, Littrow wavelength of field widened interferometer, different defocusing amount and pantograph ratio of imaging lens are analyzed. In order to verify the theoretical analysis, thermal-vacuum experiment is performed. The results show that the spec-tral deviation and profile are matched with theoretical analysis, and spectral stability is less than ±0.01 nm under the temperature from 19 ℃ to 21.2 ℃ by the substrates made of fused Silica (Corning 7980 0F). Quantitative analyses provide theoretical basis for the thermal control requirement and Littrow wavelength selection in normal atmospheric pressure.