Thermal shift assays (TSAs) are among the most commonly used biophysical approaches in drug discovery in both academic and industrial settings. However, the most common interpretation of the data generated by a TSA is purely qualitative, using only the change in melting temperature (ΔTm) as a metric. This has left many questions surrounding the interpretation of the data as well as whether the TSA truly correlates with other assays. TSAs also lack theoretical descriptions of the melt behavior of proteins in the presence of multiple ligands. Here we describe a novel simplified analytical framework based on "pseudoisothermal" models as well as exact thermodynamic descriptions of protein-ligand melt behavior rooted in changes in the entropy of melting. We show how the models are broad and independently applicable, in that they can describe the behavior of any macromolecule such as a protein or DNA and demonstrate good correlations with other techniques. These models are shown to give good descriptions of assay systems containing single or multiple ligands and can determine the mechanism of interaction. The models are derived from first principles, and the theoretical justification is discussed.