To decrease the power consumption of data centers, coordinated control of air conditioners and task assignment on servers is crucial. It takes tens of minutes for changes of operational parameters of air conditioners including outlet air temperature and volume to be actually reflected in the temperature distribution in the whole data center. Proactive control of the air conditioners is therefore required according to the predicted temperature distribution, which is highly dependent on the task assignment on the servers. In this paper, we apply a machine learning technique for predicting the temperature distribution in a data center. The temperature predictor employs regression models for describing the temperature distribution as it is predicted to be several minutes in the future, with the model parameters trained using operational data monitored at the target data center. We evaluated the performance of the temperature predictor for an experimental data center, in terms of the accuracy of the regression models and the calculation times for training and prediction. The temperature distribution was predicted with an accuracy of 0.095°C. The calculation times for training and prediction were around 1,000 seconds and 10 seconds, respectively. Furthermore, the power consumption of air conditioners was decreased by roughly 30% through proactive control based on the predicting temperature distribution.