Due to various engineering applications, spontaneous bubble movement on the heated surface has brought huge attention. This work numerically studied the bubble migration driven by the thermo-capillary force under the temperature gradients perpendicular to the gravity direction. This problem is constructed in a two-dimensional domain, and the volume of fluid (VOF) method is adopted to capture the properties of the bubble interface between the vapor and the liquid. One still vapor bubble is initially positioned at the center of the liquid domain, and the temperature gradient is applied to two side walls. The results show that the bubble with a size greater than the capillary length can only oscillate near the initial position even with a larger temperature gradient. The deformation of the bubble such as spheroid and spherical cap can be found around this regime. However, the movement of the bubble with a size smaller than the capillary length is significant under a higher temperature gradient, and it remains a spherical shape. The coefficient of thermo-capillary force (C_Th) is defined within this work, and it is found that a larger Weber number ($W_e$) accomplishes a larger C_Th. This work may provide more precise guidance for smart bubble manipulation and critical heat flux estimation for future nuclear reactor design.