Cheddar is definitely ok to store at room temperature. That is how you age the stuff. It's better to store it at 55 degrees while aging it, but it will store as long as things don't get too hot. In fact, people have been storing cheddar without refrigeration for a long, long time.
In general, you can store any of the hard or aged cheeses like this.
And yes, I know that this is a very old thread.