Steam iron comprising a sole (1) in thermal communication with a heating body (5) equipped with a steam chamber (53), the steam chamber (53) communicating with a reservoir (7) by means of a supply circuit comprising a flow control valve (10) whose degree of opening is controlled by a thermally deformable element (16) in thermal communication with the heating body (5), characterized in that the opening of the control valve (10) is braked, beginning at an intermediate temperature, by a stabilizing element (18) that exerts a force that opposes the force generated by the thermally deformable element (16).