You seem very confident that a human can't catch a dog on a hot day. I hate to be that person, but do you have a source for that?

I've gone running with plenty of different dogs in temperatures of above 30 degrees over the years. Smaller or stockier dogs (like a staffy) fade very fast. Within a couple of kms. Working breeds (retrievers/poodles/kelpies/collies) will leave you in their dust but this is why the endurance hunting hypothesis relies on efficient tracking while running. If they're running on the lead, especially when it's a bit hotter, they seem to lose it after about 10kms. On a cooler day these same dogs would leave me dead.