This is just the kind of heat that tomatoes,peppers and eggplant love but you have to ease the young plants into the full sun environment or they will scorch.
Don't water the leaves of the plants, try to hand water under the plants until the stems and stalks get woodier and the leaves are adjusted to the intense sun.
Go for it but give them bright light to am full sun to mid day full sun (with afternoon shade) while still in their pots.

Go ahead and plant some tomato, peppers and basil - they'll be behind everyone else's but they'll do fine. The tomatoes may not ripen fully until things cool down a bit (they hate hot nights). Now is when people plant okra and purple hull peas so you're not too late for them.

You can try Trombone Squash instead of all the normal stuff. It isn't recognized by Squash Vine Borer so is kinda immune to their attacks. It grows more like gourd and the vines can be 75 feet long so plan accordingly. Eat the fruit like a cucumber when they are cucumber sized or like zuke when they're a little bigger, or as a winter squash after they mature - a very versatile fruit. They even stay firm when cooked.

Wyatt-Quarles Seed Company has a Vegetable Planting Guide that gives dates for the Piedmont. You neglected to say where you were so it may be off a little. Google them. Great list. If this is your area, you are probably only a week late, so why not go for it, but you are only a month early for starting fall crops.

By the way (and I admit I don't really understand these squash moth borers), I think that they show up in mid to late May (or whenever squash start producing) if they are started on April 10th. Thats when they get my plants. Last 2 years I sprayed the roots with seven bracketing that time. So far so good, this year. Other than the poison, I was suggesting that starting late might be good for avoiding the borers.

Thanks, Dottie! I did harden off the few tomato seedlings I'd started. They're in the bed and doing pretty well so far.

You could start your fall garden seeds indoors now to be ready for planting out in a month or so. I have brussell sprouts, broccoli, cauliflower, and cabbage seedlings growing under lights now, to be planted out in July/Aug. I also plant the fall carrot crop in early July. I sow the seed a little deeper (to get the seeds down to the moisture, which is deeper in the summer) and then keep them covered with wetted burlap until they sprout, and then keep them under row covers for a few weeks. I also wait until July to seed my pumpkins (so they are ready for Halloween). I save my tuna cans to use as collars as protection against SVBs. And cow peas (black eyed peas) can be planted just about any time. I use them as a cheap cover crop between plantings. I buy them at the grocery store for $1.50 or less per bag. If you give your plants some shade early in their lives, you can still plant just about anything that matures in less than 120 days. We don't usually get frost here in the Charlotte area until mid to late Oct.