Spatial heterodyne Spectroscopy is an interferometric technique to achieve many hyper-spectral detections that have been developed for several decades by J. M. Harlander, F. L. Roesler et al. In particular, passive hyper-spectral spatial heterodyne spectrometer (SHS) is significant instrument for space applications to measure colume densi-ties of trace gases (CO₂, CH₄, CO), mesospheric OH density, global chlorophy II fluorescence and so on from recent information and progress report. Hence, the recovered spectrum of SHS also depends on its thermal-vacuum en-vironment. Thermal-vacuum environment adaptability is one of the key performances for hyper-spectral instru-ment, and SHS should provide high spectral stability especially for space detection of atmospheric trace gases. In this case, the spectral band spans 757 nm~771 nm with a spectral resolution of ~ 0.03 nm, even though an ex-tended source (extent of ~73 mrad, entrance diameter of 21 mm) is used. This channel for Oxygen (O₂) measure-ments is intended to investigate influence on Carbon Dioxide (CO₂) column abundance including atmospheric pa-rameters and surface height. Based on the research of the spatial heterodyne interference principle, simulation test in thermal-vacuum environment and quantitative analyses are carried out. The relationship between environmen-tal changes and the divergence half-angle of collimating lens, Littrow wavelength of field widened interferometer, different defocusing amounts and pantograph ratio of imaging lens are analyzed. With low thermal expansion co-efficient of 5.7×10^-7/K and high thermal refraction index of 9.2×10^-6/K, Fused Silica is well suited for grating sub-strates with high groove density, but it is not necessarily the best choice for beamsplliter and field widened wedge. In order to verify the theoretical analyses and determine if SHS performance would achieve its science goals, thermal-vacuum experiment by CS-800 and integrating sphere light source is performed at Key Laboratory of Op-tical Calibration and Characterization (KLOCC) of Chinese Academy of Sciences (CAS). The results, especially for relationship between recovered spectral profiles and different out-of-focus amounts due to optical degradation of interferogram modulation in the harsh space environment, show that the relative spectral intensity deviation and spectral profile are matched with theoretical analysis, and spectral stability is less than ±0.01 nm under the tem-perature from 19 ℃ to 21.2 ℃ by the substrates made of Fused Silica (Corning 7980 0F). Quantitative analysis provides theoretical basis for the thermal control requirement and Littrow wavelength selection in normal at-mospheric pressure. SHS is well suited for low light and high spectral resolution detection, but active thermal controller, calibration and correction under on-orbit conditions are necessary for space applicaitions.