  We prove the existence of solutions of the reduced Hartree-Fock equations at
finite temperature for a periodic crystal with a small defect, and show total
screening of the defect charge by the electrons. We also show the convergence
of the damped self-consistent field iteration using Kerker preconditioning to
remove charge sloshing. As a crucial step of the proof, we define and study the
properties of the dielectric operator.
