Warm dense matter is a high-energy state with characteristics of both solids and plasmas. It is found within planetary interiors, created during shock experiments and observed along the path to ignition of inertial confinement fusion. The effects of these environments' high temperatures and pressures demand a mixed quantum-classical treatment. Due to this complicated behavior, simulation of warm dense matter is notoriously challenging for both condensed matter and traditional plasma methods.<br /> One of the most successful methods to date for modeling warm dense matter uses density functional theory to describe the electrons within a material and classical molecular dynamics to describe its ions. We know, however, that this treatment ignores an important piece of the electronic energy's explicit temperature dependence. In this talk, ensemble and other temperature effects on static and time-dependent electronic structure are examined through the lens of mathematical density functional theory, producing a method to generate new exchange-correlation free energy approximations. In addition, a method uniquely suited to warm dense matter simulation will be presented: finite-temperature potential functional theory. Highly accurate, systematically improvable and computationally efficient, it bridges the theoretical gap between condensed matter and plasma treatments and skirts the computational bottleneck of high-temperature density functional theory.