A kinetic description of non-equilibrium processes using particle methods is applied to the investigation of electron gas temperature characteristics in the n-GaAs vacuum structure under conditions of field emission. The details of n-GaAs band structure and all essential types of electron scattering are taken into account. Based on the results of calculations, the following conclusion is given: in passing from room to liquid-nitrogen temperature the impact of L-valley electrons on the emission process increases in importance, whereas the contribution of the thermalized Γ-valley electrons in the emission current is reduced. At the nitrogen temperature the process of electron field emission is almost totally defined by the hot L-valley electrons.