I am guessing, but don’t want to assume, that you’ll be freezing your butter when you reach your final destination. Yes? If so 'Id probably freeze it before I left NYC so that is starting out as cold as possible.
Where will you be staying for the nights your are on the road? If there is a fridge/freezer would it make sense to move your precious wares overnight to rechill? The transporting and opening the cooler may do more harm than good though. @Auspicious - your thoughts?
Good luck with your trip and move. I’ll be looking for any road-trip food reports.
