We propose a novel network model for real-time prediction of temperature distribution in a data center so as to allow energy-efficient task assignment and facility management. We model various physical relationships in the data center as a network, including heat movements caused by airflow and heat generation by servers. Since changes in temperature distribution depend on physical properties of the data center such as equipment locations and server types, model parameters (connection weights in the network) that characterize relationship of nodes are determined by a machine learning technique using actual data center operation data. The proposed method provides prediction results in a shorter time than traditional methods such as model based on computational fluid dynamics and potential flow model, while maintaining prediction accuracy. We evaluate the performance of the proposed model through comparison with actual data from our experimental data center. The evaluation indicates that the proposed model can predict 10-minute future temperature distributions in 60 places in 3.3 ms, with a root mean square error of 0.49 degrees.