The KaiC phosphorylation cycle generates the circadian rhythm without the transcription and translation of kai genes. To study the mechanism of the circadian rhythm, we use the model proposed by Kurosawa et al, describing the KaiC phosphorylation process in DD case. The temperature compensation is one of the most important features of the circadian rhythm. Therefore, some methods used to construct the temperature compensated model, have been proposed. In this paper, we applied the gain scheduling method proposed by Takeuchi to the model. In which, we focused on another essential feature named "temperature entrainment". This study investigates the mechanism of the phase shift and the temperature entrainment by using the temperature compensated model under the temperature cycle. Simulations results, including the comparison with the biological experiments, clearly illustrate the effectiveness of the proposed model.