The thermal underwater glider’s propulsion power is provided by the phase change energy storage tube. To improve the propulsion performance of the glider, it is essential to study the phase change heat transfer characteristics. This work proposes a collocation spectral method to handle the spatial derivative term and introduces a fourth-order Runge-Kutta method to handle the time derivative term. The temperature distribution and liquid volume fraction of the phase change material in the energy storage tube were numerically simulated under specific boundary conditions. The simulation results were then compared to the experimental data, and a good agreement was observed.Based on these findings, the impact of incoming free stream velocity and temperature difference intensity on phase change within the vessel was examined. The results underscored the dominance of convection in solid–liquid phase change and identified key factors influencing phase change in scenarios with Stefan numbers below 0.1342. Additionally, the study highlighted the limitations of fixed-value approximations and the nonlinear nature of phase change over time. These insights provide valuable guidance for developing phase change devices that harness volumetric potential energy aboard underwater thermal gliders.