The optical system with variable F-number can simultaneously meet the requirements of sensitivity in wide field of view and the requirements of resolution in narrow field of view, and variable F-number infrared detector is an important part of the optical system. Due to the thermal contact resistance, the temperature of the diaphragms is much higher than that of the cold shield of traditional detector, which means the thermal radiation of the diaphragms would adversely affect the performance of the FPAs. Based on the radiation theory, the effect of thermal radiation of the diaphragms on the performance of FPAs was studied from response signal and NETD, respectively. Furthermore, a MW FPAs and a LW FPAs were calculated by the theory of this paper. The results suggest that the temperature of the diaphragms must be 197K or less if the variation of the performance of the MW FPAs does not exceed 10%. And the temperature of the diaphragms must be 152K or less if the variation of the performance of the LW FPAs does not exceed 10%. The research of this paper has certain guiding significance for the design of Dewar assembly with variable F-number.