We have measured the absolute values of thermal conductivity κ and specific heat C of EuRh 2 Si 2 under pressure by newly developed three-dimensional thermal-relaxation method. Below a critical pressure P V ≃ 0.9 GPa, a clear peak corresponding to an antiferro-magnetic transition is observed almost independent of pressure, although no anomaly is detected in κ. Above P V , κ exhibits change of slope at the valence transition temperature T V , and enhancement of κ is observed below T V. The magnitude of the enhancement is increased with increasing pressure suggesting that the valence change of Eu ion associated with the valence transition is enlarged by pressure.