The athermalism of diffractive optical elements in infrared hybrid refractive-diffractive optical systems is analysed. It is shown that diffractive optical elements contribute a little to the thermal effects but their achromatic characteristic plays an important role in athermalization of infrared hybrid refractive-diffractive optical systems. An infrared hybrid refractive-diffractive optical system for 3～5 μm band with short total track is designed and discussed.