arugula, carrots and spinach too late, the heat will make the arugula and spinach bolt and the carrots probably won`t come up. Leaf lettuce is iffy, the heat makes it bolt before it gets big enough to eat.
put the radishes in in the fall, if they do come up and grow it is unlikely they will be edible, the hotter the weather the hotter the radish, I pulled the last of mine two weeks ago
field peas, black eyed peas are fine to plant now
bell peppers-I would get plants and hope for the best
Kale prefers it colder but will sometimes limp through summer
eggplant will take over, hope you like it!
chile peppers thrive in heat, I am putting in seeds for hot peppers this weekend myself
try malabar spinach, it can handle heat
okra is a sure-fire summer crop
Tally Ho!

Most pole snap beans will shut down fruit production during the dog-days of summer. There is a pole bean "Rattlesnake" that can take the humid-heat better than others. Yardlong beans and southern peas also handle the heat very well.

Cucumbers seem to bask in our hot summers. New Zealand Spinach in addition to the previously mentioned Malabar Spinach is another "green" that likes it hot.

Yellow squash and zucchini (summer squash) enjoy the heat but get huge and may use-up valuable space in your sq. ft. garden. The vining "winter squashes" love the heat also and can be grown vertically on a trellis. I make a mound outside of my boxed-in beds just for squash.

Melons produce well in the hottest part of summer. My cantaloupe grow beautifully vertically on a trellis. I make a sort of "hammock" out of my wife's old knee-high stockings so the fruit doesn't drag the vines off of their supporting trellis.

Most of my pepper production barely limps along in the heat until cooler weather returns.

I use the Kratky method in partial shade to grow Adrianna and Red Cross "butterhead" type lettuce through summer heat. I built a very simple, VERY wind resistant, shade-cloth that shades the south and west exposure to my Kratke containers. There is a guy on YouTube (mhpgardener) who gives great details on how to do the Kratky method of growing. I have never experienced a simpler more efficient way of growing "smallish" plants than the Kratky method! Most of the lettuce seed at Johnny's Seed that says it is "heat tolerant" will do well in partial shade in our climates.

I'd be willing to bet that the shade-cloth idea would probably help tremendously with pepper production during the summer-heat.