Cooling is a major component in the enormous energy consumption in data centers. Accurate evaluation of cooling inside a data center forms the backbone of all the attempts for improving cooling efficiency. Models based on computational fluid dynamics (CFD) are typically used for accurate evaluation, but have a drawback of high computation time. This paper presents a novel thermal predictor to evaluate data center cooling in seconds. The key idea is to extract information from a single instance of CFD simulation using metrics called as influence indices to build the fast thermal predictor. Then, this predictor can evaluate the cooling for altered operation of data center with comparable accuracy in seconds without the need for repetitive CFD simulations. This paper demonstrates the accuracy of the thermal predictor by comparing with CFD simulations for a sample, but realistic data center. The fast thermal predictor then successfully passed more challenging tests in a real production data center and proved its practical utility. The results of the thermal predictor compared with measurements carried out in the production data center are also presented. This fast thermal predictor is an important milestone in the development of a method for model-based real time control of data center cooling.