Proteins operate through ligand and solvent interactions governed by thermodynamics, yet the enthalpy-entropy trade-offs that guide their functional evolution remain poorly understood. The LacI/GalR family (LGF) of transcription factors provides a system for examining how these trade-offs evolve over billions of years but has seldom been studied from a full thermodynamic perspective. While the evolution of ligand specificity has been well-studied, the thermodynamic determinants underlying the changes in specificity is not well understood – especially how proteins alter thermodynamic strategies to optimize affinity. By reconstructing LGF ancestors, we reveal a shift from entropy-driven binding in the most distant ancestor, to enthalpy-driven binding in the most recent ancestor and extant LacI. The most distant ancestor is characterized by the ability to bind its ligand in an open and dynamic conformation, and we propose that entropically-driven binding is driven by the presence of entropic reservoirs. This thermodynamic binding trade-off between the most distant and most recent ancestor is in accordance with the concept of ancient life that existed in a hot Earth environment, where higher temperatures enhanced entropically-driven binding. This suggests that molecular binding mechanisms evolved not just for ligand specificity, but to adapt to environmental pressures such as cooling Earth temperatures where enthalpic binding modes are favored.