In the ground experiment of spatial infrared detection equipment, an infrared scene simulator needs to be used to generate an infrared image that simulates the infrared characteristics of a space target under laboratory conditions, and the infrared image is projected onto the device under test through a projection optical system. Therefore, this paper designs an optical projection system operating in the range of 100--300 K. The system with a coaxial Cassegrain structure has a working wavelength of 3.7--5.5 μm, a focal length of 638 mm, a field of view of 3.4°×3.4°, an exit pupil diameter of 102 mm, and an exit pupil distance of 660 mm. The Zenike polynomial is employed to fit the thermal deformation data of the mirrors, and the ZEMAX software is applied to evaluating the imaging quality of the system. The simulation results show that the modulation transfer function of the projection system at different temperatures meets the design requirements, and the projection system has been successfully applied to the ground cryogenic experiment of a spatial infrared detection device.