The quasi-neutral limit of the full Navier-Stokes-Fourier-Poisson system in the torus are considered. We rigorously prove that as the scaled Debye length goes to zero, the global-in-time weak solutions of the full Navier-Stokes-Fourier-Poisson system converge to the strong solution of the incompressible Navier-Stokes equations as long as the latter exists. In particular, the effect of small/large temperature variations are taken into account.