You could get a cooler, but it seems a little overkill. Where do you keep your food?
If it were me, I would take the amount of capsules I need for the week (M-F) and keep them in a zip lock. The heat won't have a tremendous impact if you'll be using them over the next few days, but I wouldn't recommend bringing the entire bottle with you.
Have you had any issues with the Alphamax caps sticking together?