High-temperature operation of semiconductor devices is widely demanded for switching/sensing purposes in automobiles, plants, and aerospace applications. As alternatives to conventional Si-based Schottky diodes usable only at 200°C or less, Schottky interfaces based on wide-bandgap semiconductors have been extensively studied to realize a large Schottky barrier height that makes high-temperature operation possible. Here, we report a unique crystalline Schottky interface composed of a wide-gap semiconductor β-Ga2O3 and a layered metal PdCoO2. At the thermally stable all-oxide interface, the polar layered structure of PdCoO2 generates electric dipoles, realizing a large Schottky barrier height of ~1.8 eV, well beyond the 0.7 eV expected from the basal Schottky-Mott relation. Because of the naturally formed homogeneous electric dipoles, this junction achieved current rectification with a large on/off ratio approaching 108 even at a high temperature of 350°C. The exceptional performance of the PdCoO2/β-Ga2O3 Schottky diodes makes power/sensing devices possible for extreme environments.