The stability of biocrude oil is a significant challenge for its storage, transportation, and refining. In this investigation, the thermal and oxidative stability of Spirulina-biocrude oil derived from a plug-flow continuous hydrothermal reactor was systematically studied. The biocrude oil was stored at three temperatures to simulate the winter (4 °C), spring and autumn (15 °C), and summer (35 °C) seasons, and in two atmospheres (air and N2) to simulate the conditions of a storage tank being sealed or kept open. Results demonstrated that the physicochemical properties of biocrude oil were highly influenced by the storage environment. The viscosity of biocrude oil increased with increasing storage temperature and time. The maximum viscosity (17,577 mPa·s) was observed when biocrude oil was stored at 35 °C and in an air condition over 84 days, 145% higher than fresh biocrude oil (7164.2 mPa·s). The viscosity increased by 10.9% when biocrude oil was sorted at 4 °C in an N2 atmosphere after being stored for 28 days. After long-term storage, biocrude oil still exhibited comparable characteristics to petroleum, with a slight decrease in HHV (31.36–33.97 MJ·kg−1) and the nitrogen-to-carbon ratio (0.087–0.092). This study indicated that the viscosity and HHV of the biocrude oil derived from a continuous reactor stored at 4 °C in an N2 atmosphere condition remained relatively unchanged, which enables the scheduling of oil refining production.