The cryogenic support system is one of the key components of superconducting Tokamak device. In the working process, one end of the cryogenic support system is in low temperature and the other end is at room temperature. And the longitudinal field system is cyclically changing from room temperature to low temperature, when the superconducting Tokamak device is from start to stable work. This paper mainly focuses on the compress rods of the bacilliform cryogenic support system. The transverse vibration equation of a compress rod in the periodic temperature loads was established. The first and second category of unstable region boundary was obtained. The effect of damping on the unstable region size was studied. With the increase of damping, the stable region is increasing than the case of no damping. However, in some unstable region, the dynamic stability cannot be obtained by only relying on the increasing of damping. So, a state feedback control was introduced into the system, and the original system in unstable state can be stabilized over a large range of the controlling parameter.