The global carbon cycle may involve iron carbide as a component of the Earth's inner core. In this study, we report the first experimental measurements of phonon density of states, sound velocities, and Debye temperatures of Fe₃C up to 47GPa and 1450K using the nuclear resonant inelastic X-ray scattering (NRIXS) method in a laser-heated diamond anvil cell. Within the investigated pressure and temperature range, the effect of temperature on compressional velocity v_p falls within the measurement uncertainties. The shear velocity v_s decreases with increasing temperature in a non-linear fashion: at ~15GPa, v_s decreases by ~12% between 300K and 740K; At ~46GPa, temperature produces a ~5% reduction between 300 and 960K and a ~6% further reduction between 960K and 1370–1450K. The high-temperature v_s of Fe₃C deviates from Birch's law behavior towards smaller values, potentially matching the anomalously low v_s in the inner core under the relevant pressure and temperature conditions. Our results support Fe₃C as a major component of the inner core.