At rest, the body produces about 100 Watts of heat. Pettier coolers aren’t that efficient... from what I can tell, their energy consumption is roughly equal to the amount of heat they can remove in situations like this...

So in an order of magnitude calculation, to reject all the body’s heat on a hot day would require about 100Watts... so about eight 18650 Lithium ion cells for an hour, so maybe about half a kilogram of cells.

Plus a fan and radiator assembly (roughly the size of a CPU fan and heatsink). Probably adding about another half a kilogram for a total of 1 kilogram.

EDIT: I think phase change material might be a cheaper and less noisy option... about a kilogram ice packs will also absorb about 100Wh of heat before reaching body temperature.

Now if you can get a miniaturized mechanical heat pump that has higher efficiency (day a coefficient of performance of 2-4) and you need to last for much longer than an hour, I think you can significantly beat the weight of an ice pack.... and, of course, water has a heat of vaporization of 627Wh/kg, beating both options, so simply sweating (and drinking water to replenish) is the most efficient option per kg... Evolution wins again! (Provided it’s not too humid that you can no longer evaporate sweat, in which case you can die even while resting, naked, in the shade, healthy, young, and next to a fan... which can happen if the “wet bulb” temperature exceeds 35C or 95F ie 100% humidity at 95F or 50% humidity and 115F on a sustained basis.)