Cooling devices are provided to reduce a person's temperature by evaporative, convective, and / or conductive cooling. One such device maximizes evaporative cooling by aiding the flow of air to the person and the removal of vapor-laden air from the person. An upper sheet and a base sheet are adhered to define numerous elongated, parallel, inflatable cooling chambers separated by flat connecting membranes. Ventilating cross-members interconnect the cooling chambers. Air enters the chambers through an inlet, exits the chambers toward the person through air permeable regions of the base sheet. Air heated by the person's body exits the device upward through evaporation openings in the connecting membranes. The foregoing device, or different variations thereof, may be modified for use in conductive cooling by adding an absorbent sheet beneath the base sheet, or substituting the absorbent sheet for the base sheet itself. This device directs air upon the wetted absorbent sheet to cool this layer, and thereby conductively cool the patient's skin in thermal contact with the absorbent sheet. As one example, this device may be configured in serpentine shape, with multiple winding segments. The device may include body-contour slits extending inward from the perimeter, permitting the device to conform to a person's legs and outstretched arms. Cooling devices may also include optional features to enhance thermal contact between the absorbent sheet and the person's skin, and / or to prevent water runoff from the cooling field.