In order to cool the windings, core and optionally the wall of the element (1) receiving the windings (3,4) and the core (2) as effectively as possible, conducting surfaces (5, 6, 8,15) are disposed inside said element in such a way that the flow of coolant initially passes along the windings (3,4), followed by the limbs (21,22) of the core surrounded by the windings, and subsequently the other areas (23, 24, 1). Said arrangement of conducting surfaces is particularly suitable for use with transformers having superconductive windings made of HTSL conductor material. .