In a stepped-mirror-based static Fourier transform infrared spectrometer, the collimation lens is located adjacent to the light source and the thermal radiation would lead to the partial temperature increase, and the refractive index of the infrared material unavoidably changes. Then the light beam passing through the collimation lens will induce a divergence angle, directly affecting the resolution of the recovered spectrum. Meanwhile, the angular divergence results in a displacement in the interference signal, making increasing difficulties in the interferogram processing and the spectrum recovery. In this paper, the distribution of temperature in different areas of the collimation lens is studied under the working condition, and the defocusing value of the collimation lens is 0.153 mm that is caused by the refractive index gradient of the infrared material along with the temperature. In addition, the divergence angle induced by defocusing is calculated, its distribution being nonuniform but symmetrical within the sample area. Moreover, the divergence angle brings about additional optical path difference, its effect on the recovered spectrum is analyzed. Compared with the ideal recovered spectrum, much noise emerges and the peak value is reduced in the real recovered spectrum. The spectrum-construction error of the real recovered spectrum is 18.72%, indicating that the recovered spectrum is seriously distorted, and the resolution at the center wavelength in the ideal recovered spectrum and the real spectrum are 4.71 cm-1 and 5.57 cm-1, respectively. This indicates that the spectrum resolving power is weakened. Furthermore, the reasonable temperature range is obtained by analyzing the curve of spectrum-construction error versus temperature of the collimation lens. When a spectrum-construction error of less than 5% is demanded, the temperature difference between the front len of collimation and the ambient must be less than 8 ℃. Finally, experiments are performed using a SiC rod as the light source, and interferograms are made by four steps including dark current electric noise elimination, spatial gain correction, image signal averaging, and spectrum recovery. Results show that the spectrum-construction errors (SCE) from the cold light source and non-cold light source are 8.48% and 21.51%, respectively. Although they are all larger than the theoretical value, the SCE of cold light source decreases by 13.03% compared to cooling-free light source. Hence, it is necessary to reduced the thermal radiation influence on collimation lens from the light source. This result is helpful in solving the analogous problems.