As cheese age, proteins and fats from the milk break down gradully to create flavors and texture.
It is then important to control the humidity and the temperature in your storage to gently slower this process.
Control the temperature in your storage allow you to control pathogen growth and prevent quality defects.
With high temperature your cheese can inflate. What does that mean?
Bacterias inside your cheese will activate and start processing lactose inside the cheese, by doing that they expulse some CO2 and that CO2 that will make your cheese inflated.
With high temperature your cheese can start to ooze (fat inside the cheese is "melting") and creates droplets on the rind of the cheese. This make your cheese taste rancid.
In most case, having a low temperature will be better for your cheese.
But always be careful, reducing the temperature will also bring hydrometry to your storage area.
Usually, a semi-hard, hard cheese such as Cheddar or Gouda will be better at around 10C (50F). On the other end, soft cheese such as Goat cheese, Mozzarella need to be held around 4C to 6C (39F to 43F).
The 65% to 70% moisture will allow your cheese to not dry.
Some cheese (semi-hard) can develop some "mucor" around the rind. This mucor is very spreadable and will contaminate other cheese easily (mucor loves humidity and warm temperature).
To get rid of it you need to "wash" the cheese while making sure it doesn't fly in the storage area. Add some space between your cheese to let them breathe and slowly dry.
Another thing can happen, your cheese can become creamy and you all know it is quite impossible to get our cheese back to a normal texture. The only solution if your cheese is to sell, let people know it is ready to taste.
With lower moisture, your cheese will become firmer, will dry.
Remember to cover your cut pieces of cheese in your storage with the appropriate cheese paper.