It's been in the 100s here lately, and yesterday it hit 106. My horses had a choice whether to go in their stalls, stand in shaded areas, or stay out in the sun. They chose to stand in the sun. Which they tend to choose over the other options more than not.
Now maybe my 3 geldings are just morons, but my neighbor's 5 horses did the exact same thing, so I'm thinking no shade in the 80s/90s isn't going to kill your horse as long as she has water available. They're not as delicate as we think, nor apparently, are they as intelligent.
As for the flies, get her a fly mask. I have fly predators which have taken quite a bite out of the fly population this year, but I still mask my horses during the day.