How would evaporative air conditioning work in cars?
Evaporative cooler - Wikipedia, the free encyclopedia
IMO refilling the tank with water would be a minimal hassle, but
* It might not cool enough, specially in hot yet humid climates.
* Air might get too humid, thus air exchange might be needed. It can even be combined with some short cycles of regular A/C to reduce humidity.
* Mildew and fungus might appear on the car upholstery.
* Maybe sloshing due to car movement might be an issue.