The envelope tension is governed by curvature of external surfaces and shape of the balloon which is affected by the thermal characteristic of the envelope and lifting gas. But the researches about the balloon shape and envelope tension with thermal effect are rare. Combined with the balloon geometrical shape model and thermal model, the minimizing total potential energy model is solved by numerical method to predict the balloon geometrical shape and envelope tension. The effects of the flight altitude, lifting gas mass, and flight time on the balloon shape and the tension distribution were numerically investigated in detail. The results showed that the extreme values of the meridional envelope tension appear at the top and bottom of the balloon, while the meridional tension was much greater than the circumferential tension. Furthermore, the diurnal variation of the lifting gas temperature will lead to the change of flight altitude and volume, which causes a change in the shape and envelope tension. The results demonstrated that the theoretical approach suggested a pathway towards improving the structural design for a high altitude balloon.

包层张力受外表面曲率和气球形状的控制，其受包层和升力气体的热特性影响。但关于热效应下的气球形状和包层张力的研究很少。结合气球几何形状模型和热模型，通过数值方法求解最小化总势能模型，预测气球几何形状和包层张力。详细数值研究了飞行高度、升力气体质量和飞行时间对气球形状和张力分布的影响。结果表明，经向包络张力的极值出现在气球的顶部和底部，而经向张力远大于周向张力。此外，升力气体温度的日变化会导致飞行高度和体积的变化，从而引起形状和包络张力的变化。结果表明，该理论方法提出了一条改进高空气球结构设计的途径。