The thermal and electrical properties were measured for a high entropy carbide ceramic, consisting of (Hf, Ta, Zr, Nb)C. The ceramic was produced by spark plasma sintering a mixture of the monocarbides and had a relative density of more than 97.6%. The resulting ceramic was chemically homogeneous as a single-phase solid solution formed from the constituent carbides. The thermal diffusivity (0.045-0.087 cm2/s) and heat capacity (0.23-0.44 J/g·K) were measured from room temperature up to 2000°C. The thermal conductivity increased from 10.7 W/m·K at room temperature to 39.9 W/m·K at 2000°C. The phonon and electron contributions to the thermal conductivity were investigated, which showed that the increase in thermal conductivity was predominantly due to the electron contribution, while the phonon contribution was independent of temperature. The electrical resistivity increased from 80.9 μΩ·cm at room temperature to 114.1 μΩ·cm at 800°C.