This dissertation is an accumulation of my contribution to the fundamental understanding of ensemble Density Functional Theory and ﬁnite temperature Density Functional Theory, through the use of quantum model systems. Ensemble DFT is a time-independent alternative to extracting excitation energies, and provides a way to extract multiple excitations, which is not possible with the common approximations used in time-dependent DFT. Chapter 3 of this thesis covers ensemble DFT and veriﬁes an exact exchange approximation that can accurately capture multiple excitations using the Hubbard model. Finite temperature DFT is often incorrectly confused with ensemble DFT, and refers to DFT at non zero temperatures. Its value comes from its applications to warm dense matter simulations. The last three chapters of this dissertation contain several projects in the hopes of improving the understanding of ﬁnite temperature DFT using a quantum model system in the hopes of improving warm dense simulations.