Rotating electric machines generate heat volumetrically, and are cooled by forced convection aided by the self-pumping effect. In this paper we focus on the fundamental relationship between the internal flow architecture of the gas cooled winding and its thermal performance, which is represented by the nearly uniform distribution of peak temperature throughout the winding volume. We show that the cooling passages can be sized such that the volumetric cooling is most effective. From this finding follows the number of passages and their distribution through the heat generating volume. The principle is developed analytically, and it is then validated based on numerical simulations of the cooling architecture. The paper also reports the thermodynamics basis of the self-pumping effect, and its natural occurrence as free convection in general, which includes atmospheric circulation. (C) 2015 Elsevier Ltd. All rights reserved.