Phonon partial densities of states (pDOS) of ^(57)Fe_3 C were measured from cryogenic temperatures through the Curie transition at 460 K using nuclear resonant inelastic x-ray scattering. The cementite pDOS reveal that low-energy acoustic phonons shift to higher energies (stiffen) with temperature before the magnetic transition. This unexpected stiffening suggests strongly nonharmonic vibrational behavior that impacts the thermodynamics and elastic properties of cementite. Density functional theory calculations reproduced the anomalous stiffening observed experimentally in cementite by accounting for phonon-phonon interactions at finite temperatures. The calculations show that the low-energy acoustic phonon branches with polarizations along the [010] direction are largely responsible for the anomalous thermal stiffening. The effect was further localized to the motions of the Fe_(II) site within the orthorhombic structure, which participates disproportionately in the anomalous phonon stiffening.