The traditional univariate calibration method used in measuring infrared sky brightness is confronted with many issues, and two main issues are the insufficient dynamic response of the measuring instruments as well as the influence of the ambient temperature on the measurement result. In order to extend the dynamic response of the measuring instruments, a bivariate calibration model at the constant temperature was demonstrated in the paper, and its independent variables were radiance and exposure time. Then with the experiment data acquired in many temperatures, the variation of the bivariate calibration model in different temperature was analyzed. Thus trivariate calibration model was presented at the last part, and the goodness of the fit of the model and the experiment data was best. R-square is 1.000, and the relevant uncertainties in 95% confidence degree of a, b and d, parameters of the trivariate calibration model, were all less than 0.82%, trivariate model can be degraded to bivariate at some certain temperature, the deviation of all of parameters of degraded model were less than 0.6%; Finally, with the outfield experiment of infrared sky brightness, bivariate and trivariate calibration model were validated and compared. The benefit of this trivariate calibration model is that it can extend the dynamic response of the measuring instruments, and the precision of its measuring result is not affected by the variation of ambient temperature. Hence this model can be widely used and can achieve high-precision and high-efficiency measurement without in-situ calibration.