a hair styling apparatus comprising a pair of closable jaws to engage a user &# 39 ; s hair . said jaws have complementary shapes with , a first said jaw defining a curved ridge and a second said jaw defining a curved recess . one or both of said jaws includes a heater such that , when said jaws are closed , hair is heated in a heating region between the ridge of said first jaw and the recess of said second jaw . said second jaw has a curved longitudinal surface having an active cooling region . a transverse cross section through said second jaw defines at least one s - shaped curve having a forward curve into which said ridge of said first jaw fits , and a linked reverse curve bearing said active cooling region on which hair may be cooled and curved . said heating region is located on said forward curve ; and said active cooling region is located on said reverse curve . in this way , when said jaws are engaged , a tangent to a surface of engagement of the two jaws , at a point on said forward curve up to or at a point linking said forward and reverse curves avoids said active cooling region .