We have performed in situ synchrotron X-ray diffraction experiments on TaC0.99 compressed in a diamond anvil cell along 3 isothermal paths to maximum pressure (P)-temperature (T) conditions of 38.8 GPa at 1073 K. By combining measurements performed in axial diffraction geometry at 296 K and in radial geometry at 673 K and 1073 K, we place constraints on the pressure-volume-temperature (P-V-T) equation of state of TaC in a wide range of conditions. A fit of the Birch-Murnaghan equation to the measurements performed in axial geometry at ambient temperature yields a value of the isothermal bulk modulus at ambient conditions KT0=305±5(1σ)GPa and its pressure derivative (∂KT/∂P)T0=6.1±0.5. The fit of the Birch-Murnaghan-Debye model to our complete P-V-T dataset allows us to constrain the Grüneisen parameter at ambient pressure γ0=V(∂P/∂E)V0 to the value of 1.2 ± 0.1.