Maybe a small, six-pack sized cooler, refresh with ice every morning and periodically rotate in cold beverages as you use and replenish those during the day?
Or, possibly, get a lunch thermos, put the cheddar in a baggie, in the middle, and add ice around. Thermoses insulate, so they keep your food hot, but will also keep cold food cold.
Amazon.com: Thermos 12.oz. food jar
Or, maybe, buy small quantities of cheddar on the road and eat them instead of trying to preserve a two-week supply? I’m assuming you’re talking a fairly standard cheddar, and not something that can’t be picked up on the road…..
Hook’s to release 20-year cheddar for $209/lb
(I’ve had their 15-year cheddar, at about $55/lb at the time. Fantastic!)