I also think you’re onto something here, because horses are another animal well-adapted to endurance running and they sweat like crazy, more than any other non-human mammal I can think of off the top of my head.
Monkeys sweat as well, though, and in similar ways to humans. They sweat the most in their armpits. However, they don’t sweat in the vast amounts that humans do. I think the sweat first evolved as a means of pheromone transmission, that evolved into a thermoregulation device, most notably in long-distance endurance species.
Wolves evolved during the Pleistocene epoch, though, during a series of ice ages. The ability to sweat may not have been as useful when the climate was significantly colder. True, modern humans evolved during the Pleistocene as well, but we originated in Africa, where it never really got that cold even during the ice age.
Cold weather is not without cooling requirements. Polar bears prefer to travel by swimming because on land they can overheat even in sub-zero temperatures. As I mentioned above, the combination of thick fur and sweat glands may not work well, resulting in the concentration of sweat glands on the feet of wolves. That’s pure guesswork on my part.
There’s been a lot of paleontology done with DNA analysis lately. If a team could identify the genes that create mammalian sweat glands, they could go looking for similar genes in other types of animals, doing other jobs. What do sweat glands do besides secreting water, salt, and trace proteins? (Checking wiki.)
OK. Wiki says minerals, lactate, and urea. (Hey, did you know that the glands that produce ear wax are called ceruminous glands? I amuse far too easily, don’t I?) Yada, yada - sweat glands are simple tubules . . . ah. Here’s a good bit.
So skin with glands is not restricted to mammals. I’m going to guess that “secreting tubules” go back a long, long way, and have performed many varied functions, providing all kinds of organelles that could have mutated into sweat glands. In fact, if you’re willing to shorten the tubules, most life forms have secreting pores. As an instance, fish use canal pores in their lateral line sense organ. Heck, going smaller, even bacteria and archaea useproton pumps. Plants have stoma. We are tissues to hold things in, pierced by organelles to let the right things through in the right direction, and we have been for a very long time.
Having many sweat glands are an adaption to an environment that is dry and hot. They cool the body.
They must have come in handy when our ancestors were running around the African plains hunting and gathering. Losing hair makes sweating more efficient, because the air can circulate and remove heat during evaporation.
Walking upright must have been quite and advantage as well.
Our nearest relatives, the great apes, never left the forest, where the temperature is rather more steady and it is often very humid. They stayed hairy.
Consequently apes are really bad at running marathons but rather better than us at gymnastics in the tree tops.
Why do men sweat more than women? I guess men were more adapted to hunting while women did more gathering and child care.
Anthropologists have been busy theorising about these sort of questions.
I can recommend books by Jared Diamond that cover this subject.
One is why human beings have so many sweat glands compared to other mammals.
The other is where mammalian sweat glands came from. All mammals have sweat glands, but some have more than others.
Mammalian sweat glands are just one of a whole host of skin glands that various critters have to secrete all kinds of substances. Mucus plays a huge role in the life of many aquatic creatures. They cover themselves with mucus, they make homes out of mucus, they lay their eggs in mucus, they trap food with mucus.
So our fishy ancestors, before they ever flopped out on land were covered with various skin glands. And mammalian sweat glands are just one particular type. We went from fishy things to salamander things to lizardy things, and there were already mammal-like critters back in the Permian Era, before the age of Dinosaurs.
Then a global disaster happened and almost all the mammal-like critters went extinct, and so the Dinosaurs took over.
As for humans in particular, it seems to me that there’s a connection between human hairlessness, sweatiness, and bipedalism. And humans need a lot more water than other savannah creatures.
It could be a mind-over-matter matter (i.e. “It’s not lady-like to sweat like a hog, so I refuse to do so”), but I don’t think so. Or, it could have something to do with boobs being storage facilities for sweat, like camel humps are repositories for fat, but I don’t think so. Or, it could have something to do with the average mass of males versus that of females (e.g. do the experiment with Prince, Paulie Shore and Christian Bale against Oprah, Rosie O’Donnell and [del]Chastity Bono[/del] Roseann Barr, and I believe the Lake Superior sized puddles may accumulate more under the females.