Extensions to the finite temperature Green's-function method fur the calcul
ation of equilibrium densities within the Kohn-Sham formulation of density
functional theory are presented. In particular, an expression fur the densi
ty in terms of single-particle Green's-function differences summed over all
Matsubara poles is utilized. Numerical methods for the evaluation of this
infinite sum are given. This formulation automatically includes discrete as
well as continuum states, is valid for finite temperatures, and is especia
lly well suited for high temperatures. Techniques are also presented for th
e calculation of single-pal-tide Green's functions fur spherically symmetri
c systems and arbitrary complex energies. The usefulness of these methods i
s demonstrated by their application to the problem of electron screening of
nuclei in a plasma. Direct comparison is made with previous finite tempera
ture, Kohn-Sham, wave function type calculations for protons and for neon n
uclei in an electron gas. [S1063-651X(99)07203-7].