The nonequilibrium distribution functions (NDF) for the trap states in the mobility-gap under photo illumination and zero bias voltage are derived by the constructed self-consistent drift-diffusion simulator consisted of the Poisson equation and current continuity equations for hydrogenated amorphous silicon (a-Si:H). As for the temperature dependence of the NDF, we find that the values of the NDF decrease with increasing temperature (the negative temperature dependence) in the energy region near the conduction band for p-type a-Si:H. That is the reverse of the temperature dependence of the equilibrium distribution functions (EDF) for the trap states in the mobility-gap. Furthermore, we show that the new physical characteristic is applicable to the explanation of the temperature characteristic of the photoconductivity caused by the electron hopping in the conduction band tail for a-Si:H. The photoconductivity of a-Si:H decreases with increasing temperature, which is called the thermal quenching (TQ). We show that the TQ observed in a low temperature around 200K for p-type a-Si:H can be explained by the electron hopping model with the p-type NDF having the negative temperature dependence.