Actually, evaporative cooling is one of the most ideal ways of managing hyperthermia. It is also one of easiest and non-invasive methods.
The human body is constantly utilizing evaporative cooling, which is the reason a human being is secreting sweat in a warm environment.
Evaporation requires energy which, in turn, means cooling. The amount of cooling is primarily dependent on the rate of evaporation, but each kilogram of water which is evaporated has transferred about 2260 kJ of energy.
According to the reference materials I have on hand (Wyndham, et al., 1959) the level of cooling achieved by evaporative cooling can amount to 0.3 degrees celcius pr minute.
Submerging the person in ice water carries a certain risk of systemic shock and is furthermore only half as effective as the evaporative cooling with a cooling capacity of about 0.15 degrees celcius pr minute. (Wyndham, et al., 1959; Plattner, et. al., 1997; McDermott, et al., 2009)
Contrary to belief ice packing is actually not especially effective - primarily due to vasoconstriction. Whole Body ice paking reduces core temperature with about 0.03 degrees celcius pr minute (Erickson, et al, 2004), whereas strategic ice packing only manages a cooling effect of about 0.02 to 0.03 degrees pr minute. (Erickson, et al, 2004)
BTW, the wording "tepid" in conjunction with medical procedures is normally associated with a temperature around 15 degrees celcius.
//Kim Horsevad
Sources:
Erickson TB, Prendergast HM. Procedures pertaining to hyperthermia. In: Roberts JR, Hedges JR, Chanmugan AS, et al. Clinical Procedures in Emergency Medicine. 4th ed. WB Saunders; 2004:1358-70
Wyndham CH, Strydom NB, Cooke HM, Maritz JS, Morrison JF, Fleming PW, et al. Methods of cooling subjects with hyperpyrexia. J Appl Physiol. Sep 1959;14:771-6.
Plattner O, Kurz A, Sessler DI, Ikeda T, Christensen R, Marder D, et al. Efficacy of intraoperative cooling methods. Anesthesiology. Nov 1997;87(5):1089-95.
McDermott BP, Casa DJ, Ganio MS, Lopez RM, Yeargin SW, Armstrong LE, et al. Acute whole-body cooling for exercise-induced hyperthermia: a systematic review. J Athl Train. Jan-Feb 2009;44(1):84-93.