Is there a generally accepted cutoff for when it’s just too hot to safely do aerobic exercise outside? I’m torn between “must follow the schedule” and “don’t want to die” at the moment. It’s currently 91 degrees, sunny, and 60% humidity. Too dangerous?
I don’t think so. I lived in Kansas for a few years, and while the thermometer routinely busted 100 in August, the insane roadies continued to run around my neighborhood. I think the sun poached their brains. The high school football teams kept practicing in that weather, and every now and then some kid would drop dead from heat stroke or exhaustion or whatever (I shit you not). So it can be dangerous.
But it probably depends on the individual. You’ll likely have to reduce the length or intensity of your workout to compensate for the heat. If you’ve been training a while, you’ll get to know when you’re pushing yourself too hard. (For example if you can’t catch your breath, see spots, have heart palpitations, vomit, get dizzy, disoriented or black out, you probably went too far.) As long as you listen to your body and drink plenty of liquids, you should be okay. And be sure to wear a hat!
In crazy hot weather, you might consider switching to swimming or an indoor exercise.
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IANAD. This is just my idea.
Give it a shot at exercising (at low intensity) and maybe go by how you feel. You probably won’t be able to exercise at full force, but maybe you can do an easier workout.
And please, make sure you rehydrate properly.
Or else get up in the wee hours of the morning when it’s cooler. Better yet, air conditioned gym if it’s available.
It takes at least two weeks to get acclimated to the heat. So, before you are acclimated, run short and slow, slowly building up to your regular running schedule. Drink lots of water and if doing long distances, drink sports drinks.
I run 6am, the coolest part of the day, when the temps have only been around 80F. 
(Unfortunately, the RH is 100% then.) Years ago, however, in my salad days, I would run at noon.
runner’s world magazine in the 70s or early 80s looked into this and IIRC that kind of humidity with those temps is just begging for a heat stroke. Their test subjects were the running pantheon of the time, bill rodgers etc…and even these wunderkinds, though used to it were in mortal danger. I’d advise against.
Having lived in the subtropics all my life I can tell you that the key is water. Water, water, water. No, not some darned expensive well advertised “super drink”. Just water. And never mind the **re-**hydration, (well OK, worry about that, but just as importantly) worry about the pre-hydration and the during hydration.
When I was younger I ran, orienteered, bushwalked, footballed, cycled etc in ridiculously hot and sunny and humid conditions, and you are OK as long as you have plenty of water.
There are obviously limits to that, as others have outlined, and which if you’ve got half a brain you will easily recognise at the time, but the body’s ability to cope with exercise and heat is truly amazing, as long as it can sweat like a pig without dehydrating.
The danger in outdoor exercise - besides the heat for which you can compensate - is OZONE.
On hot muggy days, if the ozone is very high, being outside, especially in urban areas, can be quite “unhealthy”. It would not be smart to do aerobics or other exercise outside.
As for the heat, you could prepare to hydrate and keep hydrated, but you wouldn’t be doing much to protect yourself from ozone.
ozone: a triatomic very reactive form of oxygen that is a bluish irritating gas of pungent odor, that is formed naturally in the atmosphere by a photochemical reaction and is a major air pollutant in the lower atmosphere but a beneficial component of the upper atmosphere, and that is used for oxidizing, bleaching, disinfecting, and deodorizing
Ozone (or ‘smog’) can be a concern on hot sunny days, especially if you have any kind of respiratory issues, such as asthma. The affects could range from feeling mild tightness or burning in the chest to a full-blown asthma attack. And I don’t have any real info on this, but I imagine that exercising in high-ozone air probably damages your lungs as much as the exercise trains them, so you might not be getting much aerobic conditioning benefit from your workout.
Because ozone accumulates throughout the day, exercising in the morning usually avoids the worst of it (and late afternoon is the worst time to exercise, early evening usually not too great either, even if it’s cooled down a bit the ozone is still around).
And Connecticut tends to have quite a few high ozone days (being downwind of NYC).
So, bottom line is it’s a good idea to move your schedule to morning workouts during summer, and if you have a choice of days, pick the one that’s likely to be cooler/have wind from NE/on a weekend.
If you want to check out ozone levels on any given day, you can start with www.epa.gov/airnow