I have been speed walking in heat and humidity, and some days it is really tough. Adapting is necessary, and being more flexible is key. Like Morningstar, I adapt my workouts as I go along if necessary. This A.M. (which wasn't that hot, at around 80, but was 100% humidity!) I planned a 5k speed walk, but after about 2 miles post-warm-up on a sunny trail (which I used because I dropped my car off for repairs nearby), I decided that that was enough for the speed, and I did the rest of my walk as a slower, longer walk).
Some suggestions:
1) take water with you, or stop along the way at a park that has a water fountain. I now have identified two parks with water in the general vicinity of my regular walking routes.
2) wear a cooling bandana : a sort of neck scarf that contains water-retaining crystals. You soak the scarf in cool water (I put it in the fridge in a bowl of water overnight) then ring it out and tie it around your neck. The coolness in contact with the big arteries on both sides of the neck cools your body down.
I tried one of these for the first time during a July 4th 5k that started at 11:00 (so it was HOT!). It did seem to help (even though I still thought I was going to die at the end, I ended up with my best time so far).
3) plan a more shady route (you may have already figured this out!). When it's really hot out, I tend to do a zig-zag course up and down tree-lined streets. It's often 5-10 degrees cooler in the shade of a big tree (or at least it seems like it).
4) as others have mentioned: hydrate thoughout the day. I like to make a pre-workout smoothie containing coconut water (for electrolytes) and chia gel (to retain hydration). Today, I had a chilled coconut water as a post-workout drink as well.
5)wearing a running cap (that shades your face and has good ventilation) might help.
6) start your run as early as possible (though sometimes going out later, and having the air temperature drop as your body temperature increases, can work well, too, but in mid-summer, that would be quite late).
