Germanium (Ge) films with physical thickness of 1600nm was deposited on ZnSe substrates by an electron beam evaporation system. The transmittance of Ge film in the range of 2 to 15 μm was measured by a PerkinElmer FTIR cryogenic testing system from 80 K to 300 K with a step length of 20 K. Then, the relationship between the refractive index and wavelength in the 2~12 μm region at different temperatures was obtained by the full spectrum inversion method fitting. It can be seen that the relationship confirms to the Cauchy formula. The relationship between the refractive index of Ge film and the temperature / wavelength can be expressed as n(λ,T)=3.29669+0.00015T+5.96834×10-6T2+0.41698λ2+0.17384λ4, which was obtained by the fitting method based on the Cauchy formula. Finally, the accuracy of the formula was verified by comparing the theoretical value obtained by the formula with the measured result.