The effect of temperature on bread mold is quite interesting. The higher the temperature, the more the mold will grow. That being said, it has to be humid. Mold grows best in warm, moist environments. That’s really all it boils down to. The colder the environment, the less mold there will be on the bread. Freezing your bread to keep it warm will prevent mold from growing until you expose it to warmth.
Keeping your bread in the fridge while it’s open will stop the mold for a little while. However, the effectiveness of fridge versus on the shelf depends on where you live. A drier climate may mean either will work, but if it’s a warm muggy environment, go with the fridge.