Buy a Frio bag. They come in 2 and 4 pen sizes; maybe others. They will keep pens cool enough from one location to another.
If you are driving just bring a small cooler with ice packs. Put unused pens in a good zip bag and keep them in the cooler.
If you’re staying in a hotel use the room refrigerator. If there’s no refrigerator, ask the front desk to put them in a fridge overnight for you. Be careful, however, the hotel doesn’t accidentally put the pens in a freezer.
Another option I’ve used at a hotel is taking a glass from your room, putting some ice in it with water, and keeping the pens in the ice bath (not entirely submerged, you do not want them to freeze) overnight.