Some comments based on my experiences. Some options are not 'lightweight' but consider them for dealing with extreme heat. Look at the 'theory' and see if you can use some adaptation of them.
For the past 30+ years I have lived and hiked in the hottest desert in North America, the Lower Colorado. Summer temps in August average 106F, 115F is not uncommon, and I have experienced a high of 125F. So here is my perspective. First of all, desert dwellers need to acclimate and accept a certain degree of persperation and hot spots. Over time, you can tolerate it better. You must stay hydrated at all times and replace lost minerals. Some sports drinks are good for this. A minimum of salt intake can be helpful, and too much salt is bad. You would be surprised how much a few Pringles can perk you up after sweating profusly for a few hours. I also avoid hiking from noon - 4pm whenever possible. With moonlight or a headlamp, I often travel at night. I usually hike in the mountains in the summer, but do make some summer desert trips.
Feet - proper fit of footwear is critical, along with moisture control. I Almost never have blister problems. Also I keep my feet in shape, by wearing my hiking footwear around town. If you have to loosen your laces, your shoes do not fit properly.
For over 20 years I used a pair of heavy leather Danner Mountain Light boots with Cambrelle linings (gasp!). I always used silk liners with a wool sock. I would switch socks several times a day and let the wet socks dry on my pack. When switching socks, I washed my feet with rubbing alcohol and added a little foot powder. This works well in temps over 100F.
I have switched to two other pairs of boots/shoes. The first are a pair of Salomon XA Pro 3D Ultra Trail Running Shoes. In the hot desert I wear silk liners with SmartWool trail running socks. In the mountains I wear SmartWool hiking socks without liners, so the sock thickness it about the same. Again ensure the proper fit. There is no loosing of laces. Either they fit correctly, or they do not. At times I do have problems with the Salomons in very sandy or nasty terrain. Sand gets into the shoes because of the breathable material. Also plants and debris can be a problem with the ankle area. Here I may use some low gaiters, but they add heat. Also, the surface temperature of the ground can make the soles of my feet unbearably hot. In these situations I wear a pair of Vasque Synergist Gore-Tex Mid Hiking Boots.
Now people will tell you about the heat problem with Gor-Tex. But I need to keep things from getting inside the boots, while dealing with moisture. These boots get a silk liner with SmartWool hiking sock. The hiking socks do better than thinner trail running socks. Again, I will switch out socks during the day and use rubbing alcohol. I know I will probably get flamed about these boots, but we are talking extreme heat up to 115F at times. These boots are only used for summer desert hiking where sand, brush, cactui and rocks are issues. I prefer the Salomons for most trips.
Frequent changes of socks and foot maintenance is not an efficient technique, but is required for preventing blisters in extreme heat.
Heat on the back - again, you must learn to accept a certain amount of heat and sweat. Your method of carrying on one shoulder works well... with light packs. I often do this with my new ULA Conduit. Hike a coule hours with it on my back, then go for a short time alternating shoulders. Then it goes back to the standard method. But at times I must carry 2 - 3 gallons, or more of water. When you need to carry a lot of water, then 'wasting' water for cooking is out. Depending on how much water I need to carry, I switch to a pack with mesh panels and a frame to support the needed loads of water. I have 3 packs for this. A Kelty Serac which weighs over 7 lbs (double-gasp!), a Deuter Futura Pro 42 which weighs 4 lbs (neither of these are 'light' packs but I am dealing with extreme heat and the need to carry lots of water), and lastly an REI Venturi 30, which weighs just under 2 1/2 lbs. The mesh panels really help with the hot back. The water weight and pack weight is somewhat offset by not needing any sleeping gear, other than a light silk sheet. No rain gear needed, but I carry a light tarp for shade or a possible monsoon rain. Again, this is not lightweight backpacking, it is survival.
Clothing. You need to really look at this. I have a dark complexion, so I usually wear a thin synthetic t-shirt for temps up to 100F. Above this temperature, one must change to something that helps reduce evaporation, which requires long sleeves. From 100F - 110F it is a Rail Riders Adventure Shirt. If I expect higher temps, it is a white Columbia Titainium long sleeve shirt to reflect heat. It doesn't breath as well as the Rail Rider, but it does a much better job reflecing heat.
Hot spots on the thighs - actually this can be worse than blisters on the feet. Constant moisture on the thighs results in fungi growth and painful rashes. Yep, it is fungus. Because my skin is usually tanned and conditioned to the sun, I can get away with shorts. And I am talking breathable and baggy. I can also get by with running shorts with a mesh liner. I never wear underwear. My legs are so thin, that the thighs never rub, but I must avoid constant wet material against the thighs. If I was prone to my thighs rubbing, I would look into a longish and the lightest merino wool underwear I could find (I have not tried this, but it would proably work). Plus, I would be willing to change them several times a day. I would also wash my thighs with rubbing alcohol and maybe even apply some sort of anti-fungal powder. If it was a real problem, I would bite the bullet and bring a small spray can of anti-fungal treatment. You only need to use it at night, and the rash will heal overnight. For many years I worked as an auto mechanic and had the fungi problem during the summer. Temps inside the garage could go over 120F during the heat of the day. This treatment worked well, after suffering many years with rashes.
Heat on the head - WIDE brimed breathable hat!!!! Again, WIDE brimed breathable hat!!!! Nix the baseball cap. I use a Tilley Air Flow. If I have ample water, I place a wet bandanna over my head and under the hat. The evaporation of the water helps regulate heat. As it dries, I soak it again.
I hope this is helpful. Again, I realize that some of these are not lightweight solutions, but they are effective solutions. An interesting perspective is Andy Skurka's Western Loop, and his section from Parker AZ to Morongo Valley CA. From Eagle Mountain to Black Canyon (areas I have hiked extensively), Andy carried 38lbs of water and a total pack weight of 50lbs, using a frameless GoLite Jam2 (ouch!). To be honest, he would have been much more comfortable with one of my heavier packs, but this was a thru hike for him. This kid is tough, and few people could have done that section. Just as you need a heavier pack weight in winter snow, you need a heavier pack weight in extreme heat.