[mchannon]

The trouble with most endothermic reactions is they involve far less energy absorbed per kg than exothermic reactions tend to emit (and their reaction rates much slower than you'd like). As a runner I'd not be too enthused about lugging around a 500g brick of goo that has the best possible endothermic heat absorption. You'd lose far more in heat dissipation potential than that brick could ever absorb, at least if it started at ambient. (Imagine how less popular ice would be if it never melted but stopped cooling).

A peltier cooler would be right out; they only work when they have an active cooling mechanism (heat sink and fan usually).

If you wanted to ditch the cooler and put together a hat or other appliance with a 3V case fan and ultrathin solar cells (CIGS probably), you'd get an excellent improvement in heat dissipation, and it would work indefinitely as long as it was daytime (probably a safe bet).

[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 ;)