Under conditions with large temperature differences, the imaging quality of an infrared optical system will deteriorate due to severe temperature changes. Large field-of-view medium-wave infrared cameras for airborne forest fire monitoring work in drastically changing environments, so the optical system has high requirements for stray radiation. In order to ensure that the optical system performs stably and with good imaging quality in the large field-of-view and the required large temperature range, a cooled medium-wave infrared optical system is designed based on athermalization and the comprehensive evaluation method of stray radiation based on noise equivalent temperature difference. The optical system consists of 6 lenses and 1 filter with working wavelength of 3.7-4.8 μm, F-number 2.5, focal length 62.5 mm, and field of view 14.36°×10.87°, respectively. The pixel resolution of the medium-wave cooled detector is 640×512. By using a combination of silicon and germanium materials and reasonably distributing the optical power, achromatic aberration and athermalization designs are realized. Through cold reflection optimization and cold aperture matching, stray radiation noise in the system is well-suppressed. By a bit of aspheric optimization, higher-order aberrations are corrected based on the requirements. The results show that the imaging quality of the optical system is stable and good in the temperature range of -55~+70 °C.