We have studied the effect of population inversion associated with the electron and hole injection in graphene layer n-i-p structures with split gates at room temperature. Considering the transverse electric field screening of the n-section, we calculated the dependence of the electron-hole effective temperature and optical phonon effective temperature on the gate-voltage. It is shown that the injection can lead to cooling of the electron-hole plasma in n-section to the temperatures lower than the lattice temperature. The current-voltage characteristics, and the frequency-dependent dynamic conductivity are calculated, the frequency-dependent dynamic conductivity can be negative in the terahertz frequency range at a certain applied voltage. The study demonstrates that electron-hole plasma cooling can enhance the negative dynamic conductivity effect and improve the feasibility of terahertz lasing.