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It has been observed that a gas turbine will have an obvious low generation efficiency if the inlet air temperature is high. To address this issue, many gas generators in warm areas are equipped with cooling systems to lower the inlet air temperature and to increase generation efficiency. However, neither the impact of air temperature nor the operation of cooling systems has been analytically investigated in existing unit commitment models, which may produce generator schedules that are infeasible or cause unavoidable costly market purchase. In this paper, we first build mathematical forms to capture the operations and costs of running cooling systems. Then we develop a stochastic unit commitment model, including operations and costs from cooling systems, for uncertain demand and temperature. Finally, a set of computation results based on a real power system are presented to show the value of cooling systems as well as the effectiveness of the optimization approach.