I think the smaller, heavier breeds shouldn't really be doing it. In reality, most of the tiny breeds should stay away from running, just because of the leg span and amount of effort required.
In peak heat season, it's also best to really, really research the hell out of what you should do to make sure both you and Fido are in good health and hydrated at the end of any activity.
My parents' dog, a 40lb Aussie Shepherd and Lab mix, has a more Aussie build but Lab look to her. Which is to say, she is shorter than most labs, and not as built/wide as most Labs. She isn't svelte, she should be like 5lbs less, but you get the idea I hope.
When I ran with her, she didn't run. She trotted.
Her run speed would be my outright sprint, holy shit please don't eat me speed.
I felt ashamed by her trot. I was like, I'm not even really pushing her. lol
Then again, she did pant for a good hour afterward, perhaps slightly less.
When I took her running, I gave her an "energy treat" of some sort, kind of like an energy bar but for dogs, perhaps a half hour prior. Which, if you have your dog on a twice a day feeding schedule, depending on the timing of extra activity, it's a good idea to supplement with a little extra energy.
I'm curious to know about the "almost accidentally killed."
Did the dog like literally collapse and you could tell the dog was having some serious negative reactions? Or was it more, this dog is so damned exhausted it can't stop panting even an hour later, and won't hardly budge except to drink water?
It's just out of shape, if it's the latter. Like humans, you also have to ease into it - and doing so at peak heat also means easing into it WAY SLOWER than at other times of years.
If you, as a human, haven't ran in a year, you don't expect to go run a 5K on the hottest day of the year and expect to not collapse and/or turn it into a complete walk event a quarter mile in.
Most neighborhood walks for dogs also tend to be a slight trot for the smaller dogs, so if doing that on peak, it's best to take it easy still and make slow progress toward more activity. Even then, due to canine physiology, some dogs it is definitely not recommended to put under physical stress at peak heat except for only brief moments.