Electrical and trap characteristics of a large-size (2 × 2 mm2) β-Ga2O3 Schottky barrier diode (SBD) from 50 to 350 K have been reported. The ideality factor (n) decreases from 1.34 to nearly unity as temperature rises from 50 to 350 K, demonstrating near-ideal Schottky characteristics. The leakage current at cryogenic temperature (100 K) was significantly suppressed, indicating excellent off-state blocking performance at low temperatures. The weak temperature dependence of the carrier concentration (NS) and Schottky barrier height (ΦB) infers stable electrical characteristics of the β-Ga2O3 SBD. The stressed current density-voltage (J-V) and on-the-fly measurements reveal reliable dynamic performance under harsh low temperature conditions. Via deep-level transient spectroscopy, an electron trap, which is related to the dynamic performance instability and Lorentzian hump in low frequency noise spectra, is revealed for a β-Ga2O3 epilayer. The study reveals enormous potential of the utilization of a large-size β-Ga2O3 SBD for extreme temperature environments.