1. A method for operating a gas turbine engine including a compressor, a combustor, and a turbine, coupled together in serial flow arrangement, and a fuel heating system including a heat exchanger and an economizer, said method comprising: channeling fuel though the heat exchanger; channeling a flow of working fluid though the heat exchanger to facilitate regulating the operating temperature of the fuel and the operating temperature of the working fluid; regulating the flow of working fluid through the economizer to facilitate regulating an operating temperature of the fuel channeled though the heat exchanger; and channeling the fuel and the working fluid into the gas turbine engine combustor to facilitate increasing a fuel efficiency of the gas turbine engine.