Okra was one that came to mind here. Also sweet potatoes and Malabar spinach vine. Of course all would take extra care with watering. Also many that garden in the hotter climates will put up shadecloth to protect the plants from the intense sun.
I live in South Texas and we are getting 95 degree days this early. I have a garden patch that only gets 3 hours of sun and its doing great. I planted Tami G grape tomatoes and they are producing faster than my family and our neighbors can eat. Also have several peppers that are doing quite well.
I think the high UV allows 3 hours to be effective...Just a guess of course and the shade protects it from an all day hot sun...
So give it a shot, if you have an area around the house that receives a short amount of sun it worth a go at it, I did.
Also you can give the classic southern plant the Cowpea AKA black eyed pea a chance. They grow well in poor soil and take the heat...
You can work up your soil, add lots of organic material then mulch around your plants once planted and watered. The mulch will keep the soil cooler and hole moisture. You will have to water well regularly. What kind of crops do the farmers there grow this time of year? that would give you a clue as to what is possible. You can also utilize shade on your property to keep the garden cooler. You will not likely grow lettuce well but peppers, tomatoes eggplant all might do well with a little experimenting
Whatever you plant now from seed I don't think will take as it's to hot to germinate. Being up State from you I know how the weather is as yesterday we hit 103 and today they're saying hi 90's. I'm at the stage of the season that I have to pitch a shade cloth over my cucks, squash's as they just wilt from the sun and heat. Surprising that within a hour of doing this the plants are happy happy. You may have to do the same.
Indio-Coachella, Ca dry dry heat, all night long. Most of the gardening is done in the lower valleys farther hidden from that stretch of sweltering. Like out toward Blythe, or south- you are going to need to create a micro climate to nurture thru summers. And the nights get so cool everywhere but there! I was thru there a few weeks ago, 109* til 2 am, had to go find sunscreen. Some herbs will do okay there-with shade and attention, but winters are better gardening.
I live in Fallbrook , Ca and its hot here, I try to work early in the mornings
or late after noon. I water in the mornings. I plant mainly, beans , Tomatoes,
peppers, squash, cucumber. I hope this will help you, because of the high temps I recommends not trying to work to long in the SUN. Good luck in your garden...