A rotary electric machine which is smoothly operated with high efficiency by adequately controlling the cooling gas flow as needed to keep the highest temperature inside the rotary electric machine below a predetermined limit. The rotary electric machine includes a stator with armature windings wound around a stator core, a rotor placed inside the stator in a rotatable manner, and a cooling device for controlling cooling gas flow. It further includes a device for measuring an ambient temperature and a device for detecting armature voltage and/or armature current and/or field current. The temperature inside the rotary electric machine is calculated from the measured ambient temperature, detection value by the detecting device and an directive value of cooling gas flow. And a calculated suitable value of cooling gas flow is determined according to the calculated temperature inside the rotary electric machine.