A solid electrolyte fuel cell system includes a reformer to produce a hydrogen-rich reformed gas from fuel, oxygen and water, and a stack structure including a stack of fuel cell units each receiving supply of the reformed gas and air, and producing electricity. The fuel cell system further includes a reformed gas cooler to cool the reformed gas supplied from the reformer to the stack structure, and a temperature control section to control operation of the reformed gas cooler in accordance with an operating condition such as a request output of the stack structure. The reformed gas cooler includes a device such as a heat exchanger for cooling the reformed gas with a coolant such as air.