Thermal gradient is an important factor causing degradation in the image quality of telescopes. In order to ensure the accurate alignment of the primary focus unit and the primary mirror, the hexapod platform (as a corrector) is investigated in this paper. First, a ground-based telescope with 2.5 m aperture and 3.5 deg field of view is described. The telescope is under construction, and it is expected to be finished in 2023. Secondly, the hexapod platform with flexure hinges utilized to adjust the primary focus unit is proposed, which is applied as a corrector. Then, the inverse kinematics of the platform is established and an open-loop control system is built based on it. Finally, the cryogenic performance test for the hexapod platform is performed. The experimental results show that the resolution and repeatability of the translation for the hexapod platform can be achieved at the micro-meter level. The resolution and repeatability of the rotation can be achieved at the arc-second level. Therefore, the cryogenic performance of the hexapod platform can meet the optical imaging requirements of the wide-field ground-based telescope. The kinematic analysis and cryogenic performance tests in the paper provide a technical reference for the precise alignment of the primary focus unit and the primary mirror, which can improve the imaging quality of the telescope.