I’m sure there is a very wide range of correct answers depending upon the person, so let’s use me as the example.
I want to run this afternoon, because I haven’t since Sunday and I itch. Waiting until evening is impractical. Obviously it’s super-hot, with a high heat index which maybe doesn’t scare me as much as it should.
I am in decent condition and accustomed to running for as long as hour when the temperature is in the low 90’s. Right now it is 98, with a heat index of 102.
Do I need to worry about a half-hour or 45 minute run on shady trails, if I am already well-hydrated and take 1.5 litres of water along?
Shade makes a huge difference as well as staying hydrated. What are you carrying the water in?
Add ice to the water, it will help keep your temp down.
We have high temps here and I used to run with a Camelback.
When I was in college, I ran myself into heat exhaustion by around mile four of a track 10K, maybe 21 minutes or so. Temps that day were high 80’s.
Figured **runner pat **would show up 
Hydration pack for the water, ice is a good idea.
4 miles in 21 minutes is a pretty hard run, I won’t be pushing that hard! Can’t for one thing…
I’m always pretty careful, the last time I felt iffy I stopped and walked back. Can heat exhaustion hit all-of-a-sudden, or is it pretty obvious that it’s setting in…nausea, weakness etc. I can see a gradual onset if one was just outdoor doing moderate work.
It was a track race, not a training run.
In my case I noticed nothing out of the ordinary until within the space of a half lap, I started feeling dizzy, collapsed to the track and started vomiting.
I think the answer is conditioning. When I lived back east I ran daily in both the frigid winter, and the hot, humid summers. Because I did it daily for years, I acclimated. One can acclimate to various types of stress.
Here in Arizona with temps over 100, and often over 110, many of us do strenuous physical exercise. I always wear a cap and shirt with a SPF of 35, slather on sun block, and carry a lot of water. I fill my water bottles about 1/4 full and put them in the freezer. Then in the morning, fill them up with water, and drinking icy water does help. If you get too hot, pour water over your head an cap, and let it evaporate.
I have hiked in the heat for as long as eight hours. A very few times I ran low on water, and could feel a weakness and weariness, which i suppose might have been the beginning of heat exhaustion, but the next day I felt fine.
As to staying in the shade, there ain’t no shade out here. 
Running frequently in the heat builds up more capillaries near the skin, which helps dissipate heat.
It’s been getting hotter and hotter. I slept with no AC, just a fan. My morning pulse is usually 40BPM. On Wednesday morning it was 83. I know something was wrong and went for the morning run anyway. It was really a forced run. I got home and turned up the AC for days now. It took about 36 hours to get the pulse down and in rhythm. I don’t care to repeat this situation. Normally I adjust the high heat after a few minutes of exercise. Everything seems back to normal including that adaptation. I’ve seen the heat strike very fit runners out of the blue. Do what you can to hydrate and go out to see what happens. Be ready to back off if you get dizzy or have a racing pulse.
Took it nice and easy for 50 minutes, felt great at the end! Drank every drop in my hydro-pack though, going to get a water bottle or two before I go again Sunday. Shady mtn. bike trails with a bit of a breeze helped. Felt brutal when I would break out into the direct sun…no way would I try that for an hour.
Thanks for the input, everyone.