(How) can I keep cheddar in a car in summer for 2 weeks
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!)