I drove from Alaska to NY with bettas in January. Are you someplace warm or cold? I recommend keeping them in the front seat, by the heater.
I had two of those coolers with 23 of my bettas in their cups WITH heat packs and all but 4 froze. The Therometers I had in the coolers said 34 even with several heat packs in each cooler. I ended up having to hold the remaining 4 on my lap for the remaining 8 days.
I also kept a syringe with them so I could easily scoop out poops and had a 2 gallon storage container so they could streatch their fins out a bit when we stayed in hotels. After their free swim time, I put them back into their cup with the clean water.