Information about stability ranges for various phases is crucial for materials design and process engineering. These stability ranges are represented by phase diagrams, which are constructed by means of appropriate modelling approaches using thermodynamic databases. Thermodynamic functions of crystalline solids can be derived from heat capacity data. Standard heat capacities of elements can be described by a Debye-Einstein integral in the temperature range from 0 - 300 K. This fitting approach avoids overfitting, and the correlation of fit parameters is small compared to splines or an Einstein function with a polynomial extension.  It is a challenge to combine these low temperature heat capacities with SGTE (Scientific group thermodata Europe) unary data, which are usually polynomials valid above 298.15 K. To this end the low-temperature fit can be supplied with constraints in which deviations in the function and the temperature derivative at the transition point are penalized. If this causes the low-temperature fit to deviate too much from experimental data, a switch function can be implemented as an alternative. As examples standard heat capacities for some elements are obtained from this fitting procedure and the standard enthalpies, entropies and Gibbs energies are calculated with their uncertainties. It is recommended to use the coefficients of the Debye-Einstein integral fit for describing heat capacities in the range of 0 - 300 K. The derived thermodynamic functions are then obtained on the same theory-related semi-empiric basis.