An important distinction has to be made between insulin that is in use now, and that which is in storage for later use. For example, I use Lantus and Novolog.

For the in use insulin, they both will stay effective for their 28 day life if maintained below 86 degrees Fahrenheit.

For storage, unopened, they need to at 36 - 46 degrees Fahrenheit.

So, for your folks and location, their in use insulin might be cooled by evaporation cooling and fan, but that is highly dependent on the specific conditions.

For storage, to get below 46 F, I think refrigeration is the only way in your situation. Refrigeration options have been mentioned above; some are pricey. But if power is available, a small/cheap "dorm room" fridge should do the job, as long as it is a compressor type. Thermoelectric coolers are usually limited to a number of degrees below ambient temperature, and in the summer in Arizona, may not make below 46 F.