A wholly ab initio method for deriving chemical thermodynamic data for inorganic crystals is a useful tool for theoretical research in material science. In this work, all electron density functional computations together with phonon vibrational analysis were used to derive thermodynamic profiles of two polytypes of SiC (3C and 2H) at real temperatures. This included standard Gibbs free energy of formation ( ) and enthalpy of formation ( ) values from 0 to 1000 K. Ground state properties were computed by the full potential linearized augmented plane wave method. Temperature effects were obtained by direct method computation of harmonic vibrations. To obtain and similar computations were also carried out for the reference state elements, Si (diamond) and C (graphite). Derived values include entropy, specific heat, enthalpy increment with temperature, absolute total enthalpy, internal energy and free energy, standard enthalpy of formation and standard free energy of formation for temperatures from 0 to 1000 K. Computed values are in very good agreement with the experimental data. This study demonstrates the utility of ab initio methods for deriving a thermodynamic data set.