NiO/beta-Ga2O3 vertical rectifiers exhibit near-temperature-independent breakdown voltages (V-B) of >8 kV to 600 K. For 100 mu m diameter devices, the power figure of merit (V-B)(2)/R-ON, where R-ON is the on-state resistance, was 9.1 GW cm(-2) at 300 K and 3.9 GW cm(-2) at 600 K. By sharp contrast, Schottky rectifiers fabricated on the same wafers show V-B of similar to 1100 V at 300 K, with a negative temperature coefficient of breakdown of 2 V K-1. The corresponding figures of merit for Schottky rectifiers were 0.22 GW cm(-2) at 300 K and 0.59 MW cm(-2) at 600 K. The on-off ratio remained >10(10) up to 600 K for heterojunction rectifiers but was 3 orders of magnitude lower over the entire temperature range for Schottky rectifiers. The power figure of merit is higher by a factor of approximately 6 than the 1-D unipolar limit of SiC. The reverse recovery times were similar to 26 +/- 2 ns for both types of devices and were independent of temperature. We also fabricated large area, 1 mm(2) rectifiers. These exhibited V-B of 4 kV at 300 K and 3.6 kV at 600 K. The results show the promise of using this transparent oxide heterojunction for high temperature, high voltage applications.