This paper focuses on the static cooling process for waxy crude oil stored in dome roof tanks. For the three phases of gas on top, liquid crude oil, and bottom water in storage tank, the VOF method is used to describe the evolution of physical quantities at the “oil–water”/“oil–gas” interface. The porous medium method is used to quantitatively characterize the sol–gel conversion process for waxy crude oil. A physical and mathematical models are established to describe the flow-heat transfer coupling behavior of the three-phase medium of crude oil, gas on top, and water at the bottom of the dome roof tank. In terms of the overall cooling process,The gas at the top of the tank has the simplest and fastest physical field evolution. It has the most uneven distribution (average temperature variance of 4 °C2), the strongest flow (average flow velocity of 0.4 m/s), the highest cooling rate (0.632 °C/h), and the lowest temperature (14.84 °C at the end). Its physical field is influenced by both the atmosphere and crude oil. The evolution of the physical field of crude oil is the most complex. It lags behind the gas at the top of tank and is directly effectted by it. Based on the evolution characteristics of the flow field of crude oil, the cooling process is divided into three stages: Stage I (0–––10 h) is the stage of convection generation and evolution in the crude oil region; Stage II (10 h − 34 h) is the stage of convection stability in the crude oil region; Stage III (after 35 h) is the stage of flow field transformation of crude oil. In stages I and II, the flow and momentum exchange at the oil–gas interface are significant. Crude oil is jointly influenced by the natural convection of the gas at the top of the tank and its own natural convection, forming a counterclockwise large vortex structure. The low-temperature area is near the central axis boundary of storage tank, oil–gas interface, and tank wall. The high-temperature area is within a range of 0.1 m − 3.3 m from the tank wall. After entering stage III, the flow and momentum exchange at the oil–gas interface weaken. The flow field of crude oil is only controlled by its own natural convection and transforms into a clockwise large vortex dominated. The low-temperature area is concentrated in the enclosed area of “oil–gas interface − tank wall” and “oil–water interface − tank wall”. The temperature field changes accordingly. Eventually, the high-temperature area is concentrated in the area slightly above the center of the tank. The physical field evolution of bottom water lags behind crude oil and is most unstable. Its cooling rate is 0.164 °C/h, slightly higher than crude oil’s 0.157 °C/h. The temperature is always slightly lower (33.47 °C at the end), and the physical field is the most uniform (average temperature variance of 0.0003 °C2), affected by the tank bottom environment and liquid crude oil.