FLY HIGH - Fly at 11-12.5 thousand feet. Standard Lapse Rate 3.56°F x 12 = 42.7F Assume SL Temp is 80F, at cruising altitude 38F. That is cooler than any AC you can put in an uninsulated aluminum airplane with bubble canopy.
AIRFLOW - Example are 12 volt battery powered or 12v DC plug in fan. Ryobi USB Lithium Clamp Fan Kit with USB Lithium 2.0 Ah Lithium Rechargeable Battery. Airflow is nice, cheap, easy and does add a modicum of additional comfort
FLY EARLY - Being outside at the airport when it's hot, is going to be hot.
You can quote me on that brilliant observation. Ha ha. Not a lot we can do about that big glowing thing in the sky during the day. The hot part is ground operations. There are ways to minimize having a heat stroke while pre-flight, taxi,, runup, and initial climb. One way is fly really early in morning when temps are at min for day.
DRESS TO BE COOL - Wear floppy hat, loose light long sleeve, a light cotton tee-shirt under (absorb sweat). drink water, try and find shade when able If you want to spray water mist on you, cooling towel (wet evaporates). Don't forget cool looking sunglasses.
SAFEETY - Compressor driven off a belt is the way to go if you had to do AC . I wound NEVER drive it off the accessory case. Not sure that is even possible. If anything happens there, your engine stops. That is sacrosanct..
ELECTRICALLY DRIVEN COMPREESSOR - 12 volt compressor technology has come a long way. I have a 12 volt frig freezer. Amazing. It cycles on and off, 30-40 watts per/hr total use average. When running on 14 volts it draws an amp or two. Very efficient. I run it at 38F and towards the bottom of the chest it is right at freezing. I can set it to freeze. Much better than an Ice chest with your food swimming in ice water.
PORTABLE AC - EcoFlow Wave 2 Portable Air Conditioner (32lbs). ECOFLOW makes solar energy products, battery power stations. Look at it. No doubt it made to run on batteries (may be dual 12v and inverted to120v AC) and be light on electrical energy draw. You do need to exhaust the condenser air. I assume baggage area and going through bulkhead to aft fuselage is likely installation. $1200 but see some half price for refurb units from factory.
Stay cool (or warm) wherever you roam with the WAVE 2. 5,500 BTUs of AC or space heating provides long-lasting, quiet comfort in a compact off-grid build.
www.ecoflow.com
SELF CONTAINED POPULAR DIY COOLER (1000's of videos and pre made products) is basically an ice chest with ice/water, and forced air blowing cool air (100's of different designs) . This is not much different than swamp cooler but uses ice. Need modest electrical power for fan, from onboard battery pack (power tool) or plug into planes Cig lighter jack.
Example:
The IcyBreeze V2 Pro is the ultimate portable air conditioner and cooler. Keep cool anywhere with this powerful, lightweight, and easy-to-use device.
www.icybreeze.com
Evaporative Coolers or Swamp cooler uses only water (no ice) and evaporation (pads). Blowing wet air inside your plane would not bode well for long-term corrosion prevention may be? They make small ones I think 12vdc and 120vac. Again power is just for fan no compressor.
AMAZON - If you search Evaporative Air Cooler or Portable Air-conditioner there are many products. Some may be 120VAC powered but could be run easily on an inverter, but I suspect the 120Vac ones have a power supply to drop down to 12 volts. So a little wiring will make a nice portable cooler. Personally I would just go with a battery powered fan like the Ryobi I mention above, and a mist spray bottle to sprinkle water on my face if needed. Again fly high altitudes and stay cool.