[cake93]

Correct me if I'm wrong, but from a thermodynamic point of view the major problem is the entropy. You can't just convert heat into any other form of energy (light) without also caring of the entropy. In the case of solving some salt in water, the entropy is going into the chaos of the solved ions (versus the low-entropy crystal). With all the other methods you need to get rid of the heat. With peltier coolers I could imaging "watercooling" the hot side.

On the other hand sweat (evaporation) is already a pretty good cooler and covering the skin with something else stops that effect. Additionally you enrich sweat inbetween which does not feel well. Completely absorbing the sweat also kills the cooling effect..

So maybe, as mchannon suggested, all you have to do is design a nice, flexible and good-looking sweatband with an integrated fan ;)