I've heard that, if the hides are different, they can be known to like one hide more than the other (feeling more secure or comfortable etc.) so will spend more time in their 'favourite'. Maybe swap the hides around and see if he goes back to the same one that's now on the warm side.
Also as Quahog said, the rock would insulate better than cardboard, so maybe it's now much warmer inside the hide so he needs to get out to thermo regulate more.