Fault detection and diagnosis are essential to the air conditioning system of the data center for elevating reliability and reducing energy consumption. This study proposed a convolutional neural network (CNN) based data-driven fault detection and diagnosis model considering temporal dependency for composite air conditioning system that is capable of cooling the high heat flux in data centers. The input of fault detection and diagnosis model was an unsteady dataset generated by the experimentally validated transient mathematical model. The dataset concerned three typical faults, including refrigerant leakage, evaporator fan breakdown, and condenser fouling. Then, the CNN model was trained to construct a map between the input and system operating conditions. Further, the performance of the CNN model was validated by comparing it with the support vector machine and the neural network. Finally, the score-weighted class mapping activation method was utilized to interpret model diagnosis mechanisms and to identify key input features in various operating modes. The results demonstrated in the pump-driven heat pipe mode, the accuracy of the CNN model was 99.14%, increasing by around 8.5% compared with the other two methods. In the vapor compression mode, the accuracy of the CNN model achieved 99.9% and declined the miss rate of refrigerant leakage by at least 61% comparatively. The score-weighted class mapping activation results indicated the ambient temperature and the actuator-related parameters, such as compressor frequency in vapor compression mode and condenser fan frequency in pump-driven heat pipe mode, were essential features in system fault detection and diagnosis.