Also many hotels have fridges in the room or another one you can store stuff in. Also if the hotel does not have one you could store it in the ops room fridge. I would guess all our ops rooms have fridges. If you pack a lunch pail and freezer packs you would be ok. You can usually find a place to store them and re freeze them.
Lastly I have heard of flight attendants using head ache bags and filling them with ice every morning and night. They say those work well.