The noise temperature Tn of n-GaAs was systematically studied as a function of the electric field and the temperature by the single particle Monte Carlo method. The noise temperature was evaluated to increase rapidly above 1 kV/cm, to reach more than 30,000 K in a pure sample at the lattice temperature of 80 K, keep that temperature above that electric field. The hot electron noise temperature was cooled down by the impurity scattering, while Tn was larger for the higher impurity concentration at a low substrate temperature below 100 K. These characteristics are in quantitative agreement with those of the experiments.