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This paper presents the modeling and measurement of a quasioptical niobium nitride superconducting hot electron bolometer mixer at submillimeter wavelengths. The modeling is performed with a distributed hot spot model which is based on solving a heat balance equation for electron temperature along the superconducting microbridge. Particular care has been taken during the modeling concerning the temperature-dependent resistance and the bias current dependence of the critical temperature of the device. The dc and mixing characteristics of this mixer have been computed and we have observed a quite good match between the predicted and the measured results for both dc characteristics and mixing performances at submillimeter wavelengths.