A cooling system includes: a core casing configured to house a compressor, a combustion chamber, and a turbine; a tail cone configured to form at least part of an exhaust passage of the turbine together with the core casing; struts configured to connect the core casing with a support body of the tail cone; a housing installed in the tail cone, configured to house an electrical apparatus; and at least one primary duct configured to connect between an internal space of the housing and an outlet passage of the compressor or a discharge port of a blower installed in a gas turbine engine via at least one of the struts and a radial outside of the core casing.