A system for cooling the skin of a human or animal user includes thermally conductive elements (120) with fluid-wicking surfaces (124), ways to flexibly interconnect the elements, methods for storing a cooling fluid and distributing it to elements (120), and ways to maintain elements (120) in contact with a user's skin. When at least portions of the elements (120) are in contact with a user's skin and at least portions of the element surfaces are wet with fluid, the evaporation of fluid from the surfaces transports heat from the user's skin into the surrounding air, thereby cooling the user. More powerful embodiments further include an air space (165) parallel and adjacent to the user's skin into which elements (120) penetrate, and a fan for moving air through the air space (165), thereby speeding the evaporation of fluid from the surfaces of the elements (120). Thermostatic or electronic means can be added to control the fan, thereby automatically cooling the user when the fan activated, and warming the user when the fan is deactivated by using the materials and air spaces in the device as thermal insulation.