I would recommend reading _Born to Run_ by Christopher McDougall. Later in the book he addresses this very topic and expands much more upon the topic of humans and long-distance running.
Humans sweat, which most (all?) other animals don't. In that way we can dissipate heat through our breath, like other animals, _and_ via perspiration, meaning it takes us much longer to overheat.
Additionally, humans stand upright, allowing us to disconnect our stride from our oxygen intake. Other animals' strides correlate (mostly?) 1:1 with the breaths they take. So when a cheetah outstretches in its stride it breathes in and when its legs come together it exhales. Humans stand upright, meaning we can breathe however we want regardless of our stride and speed. We can take deeper breaths because we don't have to exhale every time we stretch our legs.
Humans are the ultimate marathon runners, even more so than horses, evinced by the fact that there are some people throughout history who have run hundreds of miles in the course of days or weeks. There's a theory touched upon in the book about how this allowed us to dominate the animal kingdom before we even had tools. Humans could relentlessly hunt and exhaust animals as long as they could keep them in sight or otherwise keep up with their tracks.
I'm not doing the book or the topic justice, surely, but if you're interested I highly recommend the book.