Headwear (2) for removing heat from a person's scalp in order to prevent hair loss, comprising a body portion (4) for fitting over the scalp, an inlet (6) and an outlet (8), and fastener means (10) the headwear (2) being such that it opens to a flat condition when it is not in use on the person's head (12), and the body portion (4) comprises a plurality of internal walls (14) which define a passageway (18) through the body portion (4) from the inlet (6) to the outlet (8) whereby the cold fluid is able to circulate through the body portion (4), and the passageways (16) being such that they are expanded by the cold fluid and press against the person's scalp with a pressure which causes contact with the person's scalp and thereby to facilitate maximum cold transfer.