Knowledge of rock thermal conductivity is necessary to understand the thermal structure in active seismogenic zones such as the Nankai Trough subduction zone, SW Japan. To estimate in situ thermal conductivity at the oceanic crust surface in the seismogenic zone, we measured the thermal conductivity of a basaltic basement core sample retrieved from subducting oceanic basement at the Nankai Trough Seismogenic Zone Experiment input site C0012 under high temperature (maximum 160 °C) and high pressure (maximum effective pressure 100 MPa), respectively. These conditions correspond to the in situ temperature and pressure at the oceanic crust surface in the updip limit of the Nankai seismogenic zone (~7 km below the seafloor). Thermal conductivity of the oceanic basalt is both temperature and pressure dependent. In contrast to other rock types such as sandstone and granite, for which thermal conductivity decreases with increasing temperature, the thermal conductivity of the oceanic basalt increased with increasing ambient temperature. The thermal conductivity of the basalt also increased with increasing effective pressure; however, the rate of increase was much lower than that for other rocks. These new temperature and pressure effect data for oceanic crust basalt fill a gap in the research. The estimated thermal conductivity of the basalt at in situ temperature and pressure conditions was less than ~2 W m^–1 K^–1, although deformation and alteration associated with subduction could decrease pore spaces in the basalt, leading to enhanced thermal conductivity. This value is significantly lower than that typically assumed for thermal structure simulations in the Nankai subduction zone.