Mixed quantum-classical simulations of warm dense matter, necessary for planetary and fusion science, are notorious for their high computational cost. We propose a new, efficient approach to the iterated electronic structure step in quantum molecular dynamics simulations: finite-temperature potential functional theory. A basic introduction to zero-temperature potential functional theory will be provided as context for the non-zero-temperature formalism. Having established the exact formalism, the accuracy of our orbital-free method will be demonstrated on a model system using a semiclassical approximation that will be compared to both Thomas-Fermi and the next-order gradient correction. Successful implementation of finite-temperature potential functional theory for realistic systems could dramatically improve the efficiency of electronic structure calculations in the warm dense matter regime.