  Density functional theory (DFT) has become the most popular approach to
electronic structure across disciplines, especially in material and chemical
sciences. Last year, at least 30,000 papers used DFT to make useful predictions
or give insight into an enormous diversity of scientific problems, ranging from
battery development to solar cell efficiency and far beyond. The success of
this field has been driven by usefully accurate approximations based on known
exact conditions and careful testing and validation. In the last decade,
applications of DFT in a new area, warm dense matter, have exploded. DFT is
revolutionizing simulations of warm dense matter including applications in
controlled fusion, planetary interiors, and other areas of high energy density
physics. Over the past decade or so, molecular dynamics calculations driven by
modern density functional theory have played a crucial role in bringing
chemical realism to these applications, often (but not always) with excellent
agreement with experiment. This chapter summarizes recent work from our group
on density functional theory at non-zero temperatures, which we call thermal
DFT. We explain the relevance of this work in the context of warm dense matter,
and the importance of quantum chemistry to this regime. We illustrate many
basic concepts on a simple model system, the asymmetric Hubbard dimer.
