A new, least-squares optimization method with interpolation is devised to fit skeletal vibrational heat capacities to the two parameters θ1 and θ3 in the Tarasov function used for heat capacity calculations of linear macromolecules. When heat capacities are available in the proper temperature range, θ1 and θ3 can be determined uniquely in a single computer run. Appended to our Advanced THermal Analysis System (ATHAS), this new method offers an improvement in analyzing heat capacity data and facilitates the systematic study of the physical significance of θ1 and θ3 values for all polymers and related molecules of the ATHAS data bank.