Use solid blocks of ice, like 2 liter soda bottles or juice bottles.
Granted I wasn't dealing with the downright sizzle of the southwest, but I took a trip to Florida a month ago, 70's to 80's, with one cooler, a couple of frozen juice bottles and small hotel fridges to refreeze mid trip. I kept a lot of things cool for two to three days at a time. I bought two bags of ice during the 13 day trip and still had good milk for coffee on our last day.
Granted I wasn't dealing with the downright sizzle of the southwest, but I took a trip to Florida a month ago, 70's to 80's, with one cooler, a couple of frozen juice bottles and small hotel fridges to refreeze mid trip. I kept a lot of things cool for two to three days at a time. I bought two bags of ice during the 13 day trip and still had good milk for coffee on our last day.