I do hike in the summer, and live close to where you were. Here are some thoughts. Keep in mind that you were in a very dry desert. Hiking in southern Arizona during monsoon season is a lot different. I find it much more difficult to sleep in high humidity. Also keep in mind that I have lived in the lower Colorado desert for 35 years and am well acclimated.
The biggest thing is you MUST have enought water, and all water sources MUST be confirmed prior to going on your trip.
I can hike in the heat of the day, IF I have ample water. But if we are taling about 110F and higher, I try to rest in shade from about noon to 4 or 5 PM. Then I will hike until late in the evening. But not too late, because I want to start hiking before 6 am in the morning. Also, if water is somewhat scarce; no cooking. The exception for me is morning coffee.
Normally in the summer, insects are a non-issue unless you are sleeping close to a water source.
Also you need to check the weather forecast. Sometimes the temp swing can be 40 or 50 degrees, but in summer it is usually around 20 degrees.
For sleeping I have 3 options.
1. BPL 60 quilt. Light but it can be too warm.
2. A blanket like they give you on an airplane. aprox 30" X 70." Polyester blend. Weight is usually around 8-9 ounces.
3. A cotton/poly sheet. Twin size and a DARK color or it will get filthy. If it gets windy it is big enough to wrap around you so the wind does not blow it off. Also if you are near a reliable water source, you can soak it in water and wring it out. Helps you get to sleep right away and will evaporate. I have trid soaking my clothes but find it difficult to sleep at first. You will actually get cold with wet clothes at first, but I feel clammy. Wear your clothes and a wet sheet will let you get to sleep right away. Were you were, you had access to the Whitewater River and Morongo Creek. Also if your sheet is wet, it will pick up sand, especially if it gets windy. But in the morning when it is dry, it is pretty easy to shake off the sand.
Hiking clothes. If Ihave a good sun tan, then it is shorts and a Rail Riders Eco T Shirt. No tan, then a Rail Riders Eco Mesh shirt or just a plain long sleeve white dress shirt (cotton/poly). If I find a water source, then I soak the shirt. If water is scarce, I usually bring enough so I can occassionally soak my bandana which I keep around my neck. Always wear my Tilley hat. An umbrella could be a great piece of gear, unless it gets windy. I have never tried it.
Afternoon rest. You MUST have shade. The sun will be unbearable (although I can hike in the high teens, it is not a lot of fun. If I have ample water sources I sometimes hike in the heat of the day. Here a tarp is excellent. Keep it high off the ground for circulation. The goal is shade. I find my cuben tarp is tranparent and not cool. My dark poncho tarp alson gets hotter than what I like. I had a friend build me a tarp made out of Tyvek with a reflective coating. I really does a great job for afternoon shade. But it can get windy, so that is a concern. Here are some pictures of the first prototype. The tie outs are made from elastic cord so it will flex with the wind. When I tested it in my backyard, it was pretty windy and it had no side ties, so I used some ancient Visclamps… also wanted to see if it would tear in the wind. It held up. The final version has ties on the sides. A-frame is not ideal, IMO. If you can find a tree, large bush or Ocotillo set it up in lean too mode. I take a lot more cord for this than I would on a normal trip.



Don't know if you can see the details, but the elastic cord is sewn in along the complete edge. I used a Visclamp instead of the cord so I could get a taunt pitch. I also did this on the side tie outs.

Corner tie out on elastic cord. Keep in mind that this is a prototype. The final version weighs around 15 ounces. Not UL, but the shade is well worth it.
Desert hiking in the summer presents some unique challenges. But there are no crowds, and the evenings can be absolutely gorgeous. Just make sure you know exactly what you are doing. You can die from heat stroke in just a few hours.