We extend recent textit{ab initio} calculations of the electronic band structure and the phonon dispersion relations of rhombohedral GeTe to calculations of the density of phonon states and the temperature dependent specific heat. The results are compared with measurements of the specific heat. It is discovered that the specific heat depends on hole concentration, not only in the very low temperature region (Sommerfeld term) but also at the maximum of $C_p/T^3$ (around 16 K). To explain this phenomenon, we have performed textit{ab initio} lattice dynamical calculations for GeTe rendered metallic through the presence of a heavy hole concentration ($p$ $sim$ 2$times$ 10$^{21}$ cm$^{-3}$). They account for the increase observed in the maximum of $C_p/T^3$.
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