With the rapid development of information and communications technology, increasing number of data centers is required to support the cloud computing, and critical web-based services that run our daily lives. The conventional cloud data centers usually adopt computer room air conditioner or inRow units as the cooling sytem, while the rack mountable cooling unit is a more promising equipment due to the economy, exact controllability, flexibility, and scalability. To ensure the efficiency of control system in rack mountable cooling unit and the security of servers in the data centers, the information of temperature distribution is very essential. Basically, the temperature distribution could be obtained through physical sensors easily. However, considering the cost of whole system and the burden of fault diagnosis in sensor networks, the number of temperature sensors should be kept down to a bare minimum. Therefore, it is necessary to develop an effective and real-time observer to estimate the temperature distribution in the system. Besides, due to the complex air flow and heat transfer in the container, it is quite difficult to construct a physics model. To this end, a novel observer embracing data-driven model and adaptive Kalman filter is proposed in this work. Auto regression exogenous model is adopted as the framework of data-driven model, and the model is identified through a algorithm of partial least square. Moreover, to represent the nonlinear behaviors in the system, fuzzy c-means is applied for data classification and getting multiple local linear models. Finally, adaptive Kalman filter is utilized to estimate the temperature distribution on the basis of proposed data-driven model. The estimation results based on experimental data indicate the performance of proposed approach is remarkable.