I don't know if I can really give you the answer you want. Over the years I've "van camped" quite a bit, often in summer in the Southern US. But here is what I have learned...some might help you.
First, both of my Ford vans were nicely insulated. You have to beat the heat factor of direct warming of your interior space. Insulation and shade are what do this. Even a light direct sun blocking cover (canopy, tarp, old parachute) over the van with an insulating air space will help a lot.
As far as no 120vt source of power...thats really the killer as far as AC. Having and running even specialized low power AC on batteries, inverter and and solar when dry camping can be done...but is expensive and requires really more investment and space than most folks want to deal with on a van body platform. I had a small 120vt AC unit mounted in a rear window on one van...I often could find a "plug in" in out of the way urban/suburban areas for the asking. This tiny unit rocked! The fan noise also was a great masking noise for good sleeping. With energy prices where they are...a free outlet is getting hard to find. Having and running a small genny is also a pricey option - all factors considered.
What works very well is moving air. Get a good roof vent...such as a Fantastic Fan...with a reasonable house battery system and a 120wt solar panel your good to go all night. Screened windows allow air in...the vent moves it out. The "flipper/ open at the bottom" windows on most vans adapt well to velcro screens and allow venting...can be open in rain, and provide some security also.
If it is just killer hot...you might find getting out of the steel box of the van is a better option. The coolest "hot weather" sleeping outdoors with no AC is in a camping hammock...your shaded, and hanging in air.