In addition to our ability to throw shit, humans also have some of the best endurance that mammals have to offer. An example of this is the Human V Horse race in Wales. The race is a 22-mile / 35-kilometer marathon that takes place in mountainous terrain. Normally, a horse would beat a human in a race without a problem. But in a marathon, humans actually stand a chance with an occasional victor in this specific annual race. All due to our exceptional endurance.
Put the projectiles and endurance together, and we make for a terrifying hunter. Imagine you're some other animal out in the wild. Maybe you're really fast or really strong. But if a determined human really wants to try and kill you, there's no out-running it. It'll catch up eventually. And if you choose to fight the human, they'll get the first blow.
When it's hot out, the human wins. When it's cold/cool, humans can't stand a chance against the horses. Similarly, wolves and dogs can easily outrun humans in the cold, but lose to humans when it's hot.
That's because the biggest comparative advantage that humans have is actually thermal management while running, not the act of running itself.
Humans sweat. This means we can actually perform intense exercise even in heat, without overheating as easily as most other animals. Most quadruped mammals pant to cool, and have their breaths tied to their steps while running, so they can't cool themselves efficiently while on the move. Persistence hunting doesn't tire out prey, but actually overheats the prey to where they can't run any further.
Throw in the fact that we can throw, handle weapons while running, climb shit, talk, invent things, etc., and we really have been a deadly species for long before industrialization.
Do they actually allow the horses to run to exhaustion in the heat?
Googling
No, there are mandatory vet checks that can last large amounts of time that are deducted from all horses time. So the cold/heat makes a negligible difference, the horses get long rest periods either way and have historically often won even in years where it was very hot.
It's not a negligible difference. The race results for that specific race are correlated with temperature during the race. The horses naturally hold back on their speed when it's hot out, to prevent running to exhaustion. This is borne out by statistical results comparing speeds for horse races generally, not just the human versus horse race.
Note that horses generally are much faster than humans, even over distance, so the trend lines wouldn't cross unless very hot, to where it would literally be dangerous for either species to be running.
and don’t forget that humans have excellent and precise communication skills, too. At least in theory. One human might not be able to kill the wild animal, but a group can.
Tracking skills would also have to be part of the arsenal, otherwise something could just run far enough fast enough that we couldn't find it, despite our endurance.
I remember reading somewhere that the primitive human used to hunt just like that, keep following the prey in marathon, tracking their foot step, and slowly drain out the stamina of a prey. Sprinting takes a lot of energy in all animal so it kinda makes sense.
Also, we can and do eat some mild poisons because they’re tasty somehow.
I have a love of chocolate, but smaller animals can’t eat as much without severe metabolic issues that might kill them.
And capsaicin is straight-up an anti-mammal deterrent. Birds might be able to eat it with no reaction at all. Meanwhile humans just deal with their temperature receptors being freaking hacked for seemingly no other reason than fun.
Let’s also add on that humans used a tactic called “persistence hunting”, in which you follow after some animal at a brisk pace startling it every time it tries to rest. With nothing more than sweat glands, pointy sticks and ridiculous endurance, we marathon jogged some species to extinction!
Our ancestors noticed these animals that would follow us around in packs. They could generally keep up with us, form bonds easily, were pretty good at killing, and mostly ate the parts of the animals we didn't.
We just chose the ones who were coolest with us and just bred the ones who loved us the most.
There are other animals that fit this description, but dogs are the only ones that also happen to reproduce fast enough that you could feasibly notice the improvement in behavior over generations.
In soviet russia, an experiment was made to see if the domestication of dogs could be replicated on foxes, with mild success. Basically all foxes in western Europe today are in some way crossbred from the tamer foxes produced by this experiment, explaining why foxes aren't completely terrified of humans.