It is demonstrated in this work that a four parameter Debye–Einstein integral is an excellent fitting function for heat capacity values of pure elements from zero Kelvin to room temperature provided that there are no phase transformations in this temperature range. The standard errors of the four parameters of the Debye–Einstein approach are provided. As examples the temperature dependent molar heat capacities of Fe, Al, Ag and Au are calculated in the temperature range from 0 to 300 K. Standard molar entropies, enthalpies and values of a molar Gibbs energy related function are derived from the molar heat capacities and the values are compared to literature data. The next goal focuses on a seamless transition of these low temperature heat capacities to SGTE (Scientific Group Thermodata Europe) unary data. This can be achieved by penalyzing deviations in the heat capacity values and in their temperature derivatives at the transition point. Whereas the constrained heat capacities of Fe and Al mimic the experimental data, the calculated values deviate considerably in case of Ag and Au. As an alternative a smooth transition in the heat capacities and the temperature derivative is achieved by a switch function employed close to the transition region.