A density-functional theory for superconductors at arbitrary temperature is described. It leads to equations of the Kohn-Sham type, which incorporate exchange and correlation effects into the Bogoliubov-de Gennes equations for an inhomogeneous superconductor. Further, this formalism yields exchange-correlation corrections to Eilenberger's expression for the thermodynamic potential of a superconductor, and the Ginzburg-Landau equation. Practical aspects of the application of the formalism are discussed.