O.P.-- I ride in temps quite similar to that in the lower Sonoran Desert (SW AZ). Though it surprises many people, it gets very humid here in the summers. One day I recall specifically, I was driving home at 112F and it started to rain...
Anyway, the best I've tried in those conditions are (depending upon how much shielding you have available from a fairing, etc) either a perforated leather jacket like the KomodoGear Ceno I wear, or a leather jacket with super-high-flow, but closeable, vents. That over the top of an LDComfort long-sleeve turtleneck shirt completely soaked with water is about the best a person can do, IMO/E. I also have a phase-change cooling vest, and although it's very useful, I don't like it overall as well as the LDComfort. Be careful, though, a perforated jacket, or especially a mesh textile, will evaporate your cooling water TOO quickly. I ride a sport bike and basically lay on the tank in order to get what wind shielding I can from the tiny fairing & windscreen. my ~40-mile (one way) ride each afternoon sees the arms of my LDComfort shirt completely dry, and the torso pretty well dry except under the back armor. Air flow there is reduced, plus I'm sweating and keeping it wet. :|
Also, WEAR SOMETHING LIKE AN LDCOMFORT HEADLINER UNDER YOUR HELMET. That's super important/helpful to keep the body cooled.
Good luck! I don't especially like riding when it gets above 110, and it's quite un-fun above 115. It's doable, but not at all fun.
KEEP LOTS OF WATER ON YOU, OR RIDE WHERE YOU CAN GET WATER IMMEDIATELY. If you can't do this given your assignment, then don't ride if you don't absolutely have to.