One or more cooling systems for ventilating a turbine and rotary shaft of a gas turbine system is provided. The gas turbine system includes a gas turbine engine and a turbine exhaust collector in separate enclosures. A first cooling system includes an educator that sucks exhaust gas through a diffuser and directs it out of the turbine exhaust collector enclosure based on suction pressure created from the high velocity of exhaust gas. A second cooling system include struts that enable the exhaust gas to flow from the diffusers to a ventilation flow stack. A third cooling system includes exhaust gas sucked from an opening to a top duct based on suction pressure created from the rotation of the rotary shaft disposed about a coupling. A guideway associated with the third cooling system also directs the exhaust gas to flow to the top duct.