Thermal density functional theory is common in simulations of high-temperature, high-density materials, despite the scarcity of explicitly temperature-dependentelectron interaction free energy approximations and disagreement over the impact of these missing thermal effects on calculated properties. Insights from both ensemble density functional theory and the electronic strong-interaction limit can be applied to thermal ensembles, creating new approximation schemes and serving to connect these branches of formal theory with thermal density functional theory and its applications. Numerical demonstrations using the finite-temperature asymmetric Hubbard dimer and the uniform electron gas will be used to examine the advantages and disadvantages of the two approaches.