Accumulated experimental observations demonstrate that protein stability is often preserved upon conservative point mutation. In contrast, less is known about the effects of large sequence or structure changes on the stability of a particular fold. Almost completely unknown is the degree to which stability of different regions of a protein is generally preserved throughout evolution. In this work, these questions are addressed through thermodynamic analysis of a large representative sample of protein fold space based on remote, yet accepted, homology. More than 3,000 proteins were computationally analyzed using the structural-thermodynamic algorithm COREX/BEST. Estimated position-specific stability (i.e., local Gibbs free energy of folding) and its component enthalpy and entropy were quantitatively compared between all proteins in the sample according to all-vs.-all pairwise structural alignment. It was discovered that the local stabilities of homologous pairs were significantly more correlated than those of non-homologous pairs, indicating that local stability was indeed generally conserved throughout evolution. However, the position-specific enthalpy and entropy underlying stability were less correlated, suggesting that the overall regional stability of a protein was more important than the thermodynamic mechanism utilized to achieve that stability. Finally, two different types of statistically exceptional evolutionary structure-thermodynamic relationships were noted. First, many homologous proteins contained regions of similar thermodynamics despite localized structure change, suggesting a thermodynamic mechanism enabling evolutionary fold change. Second, some homologous proteins with extremely similar structures nonetheless exhibited different local stabilities, a phenomenon previously observed experimentally in this laboratory. These two observations, in conjunction with the principal conclusion that homologous proteins generally conserved local stability, may provide guidance for a future thermodynamically informed classification of protein homology.