  Finite-temperature Kohn--Sham density-functional theory (KS-DFT) is a
widely-used method in warm dense matter (WDM) simulations and diagnostics.
Unfortunately, full KS-DFT-molecular dynamics models scale unfavourably with
temperature and there remains uncertainty regarding the performance of existing
approximate exchange-correlation (XC) functionals under WDM conditions. Of
particular concern is the expected explicit dependence of the XC functional on
temperature, which is absent from most approximations. Average-atom (AA)
models, which significantly reduce the computational cost of KS-DFT
calculations, have therefore become an integral part of WDM modelling. In this
paper, we present a derivation of a first-principles AA model from the
fully-interacting many-body Hamiltonian, carefully analysing the assumptions
made and terms neglected in this reduction. We explore the impact of different
choices within this model -- such as boundary conditions and XC functionals --
on common properties in WDM, for example equation-of-state data, ionization
degree and the behaviour of the frontier energy levels. Furthermore, drawing
upon insights from ground-state KS-DFT, we discuss the likely sources of error
in KS-AA models and possible strategies for mitigating such errors.
