A capillary evaporator for a heat transfer system includes a member for picking up heat energy comprising a base (10) and a plurality of projections, each of which extends from the base to a peak (12) and the size of which decreases with increasing distance from the base, and a primary wick (2) made of a porous first material with a front face adjacent to the peak of the projections. The flanks of the projections delimit, with the primary wick, empty spaces that form steam ducts. The flanks of the projections are covered with a thin layer (3) of porous material with the thickest part disposed in contact with the primary wick in the vicinity of the peak of each projection, and the thickness of the thin layer decreases with increasing distance from the primary wick.