To prevent over-heating and moisture loss of hair being styled by the influence of heat and pressure such as by a straightener, a hair styling appliance with two clamping members at least one of which includes a heating member for clamping hair to be styled. At least one of the clamping members includes a cooling member, seen in operating direction, is behind the heating member. During the straightening process, the hair will be straightened by the hot plates and then subsequently be cooled down by the cold plates.