The temperature, pH, and salt dependence of the folding of recombinant Sac7d from the hyperthermophile Sulfolobus acidocaldarius is mapped using multi-dimensional differential scanning calorimetry (DSC) and folding progress surfaces followed by circular dichroism. Linkage relations are derived to explain the observed dependencies, and it is shown that the data can be explained by the linkage of at least two protonation reactions and two anion binding sites to a two-state unfolding process. Circular dichroism spectra indicate that a native-like fold is stabilized at acid pH by anion binding. An apparent binding isotherm surface (folding progress versus pH and salt) is used to obtain intrinsic chloride binding constants as a function of pH for both sites. A saddle is predicted in the folding progress surface (progress versus temperature and pH) at low salt with a minimum near pH 2 and 20 degrees C with approximately 25% of the protein folded. The position of the saddle is sensitive to the intrinsic delta C degrees of unfolding and provides a third measure of delta C degrees independent of that obtained by a Kirchoff plot of DSC data and chemical denaturation. The observed enthalpy of unfolding approaches zero near the saddle making the unfolding largely invisible to DSC under these conditions. The linkage analysis demonstrates that the delta C degrees for unfolding obtained from a Kirchoff plot of DSC data should be distinguished from the intrinsic delta C degrees of unfolding. It is shown that the discrepancy between the free energy of unfolding for Sac7d obtained by DSC and that obtained by chemical denaturation may be explained by the linkage of protonation and anion binding to protein folding. The linkage analysis demonstrates the limitations of using the delta Hcal/ delta Hvh ratio an indication of two-state unfolding.