Keep the cheese in the paper that we send it in. The cheese paper is a specialty paper to let the cheese breathe. Wrapping cheese in plastic will kill it and deteriorate your cheese faster.
Cheese is ideally kept at 15degs which is obviously much warmer than the fridge. Many people with the luxury of a cellar store their cheeses in there. However, ensure that the cheese does not get dried out by the fan. Also place a bowl of water in the cellar to keep the air humid. The cheese will ripen perfectly.
Like most people, if you don't have a cellar, there is nothing wrong with the fridge. Keep it in the dairy compartment as this will protect it from their air movement.
If you keep your cheese in containers, ensure you keep them in separate containers and the flavours and aromas of one cheese can penetrate another more mild cheese.