Various ankle rehabilitation robots have been developed in the recent decade to improve ankle strength and mobility and to alleviate the burdens on clinicians and physiotherapists. However, existing designs have stiff actuating mechanism, heavy and bulky electromagnetic or pneumatic actuators. This paper introduces ankle rehabilitation robot that utilizes Shape Memory Alloy (SMA) wire actuator to provide foot plantarflexion and dorsiflexion during rehabilitation exercise. SMA wire is a smart material that can contract when it is heated and expand back to its original shape when it is cooled. It also has high power to weight ratio. However, the SMA wire has low cooling rate thus limits its operating frequency. A periodical cooling mechanism is proposed here. Its efficacy is then evaluated against natural cooling and continuous forced convection. The experimental study shows promising results and demonstrates that periodical cooling has both the advantages of natural cooling and forced convection and can improve the cooling rate of SMA wire actuator.