We demonstrate a method for obtaining accurate estimates of the thermodynamic parameter values characteristic of a two-state folding/unfolding transition under conditions in which the onset of cold denaturation prevents the native state from being fully populated at any temperature. This situation occurs for proteins exhibiting low thermal stability, which may be intrinsic, the result of amino acid substitution, or the consequence of protein-solvent interactions (e.g., extremes of pH, the presence of denaturants, extremes of ionic strength). Conventional analysis of calorimetric scans obtained under such conditions yields erroneous values for the enthalpy, entropy, and heat capacity changes characteristic of the folding/unfolding transition of the protein. This paper describes for the first time the weighted average enthalpy function. In contrast to the van't Hoff and calorimetric enthalpies, the weighted average enthalpy yields thermodynamic parameter values which differ by less than 5% form the true value, even for situations in which the population of molecules in the native state at the start of the transition is half of the total.