I'm down in Florida, so I've experienced the nastiness of humitidy effecting my game, music, book, and movie collection. Even though our home is kept at a fairly cool upper 70s temp year round, humidity seems to sneak it's way in all the time. Luckily for me, my game collection was small enough to fit in a closet in my bedroom, which I keep dark all the time.
Honestly, I would very much suggest getting those games out of the basement if it's possible. Basments aren't usually insulated, which means they get hit with the brunt of both hot and cold weather extremes, which isn't great for games at all. But, humitidy is your real killer, particularly of covers, though it can lead to damaged cartridge contacts over time. If you don't have any other option than the basement I would very much suggest covering any windows around the games down there with UV blocking curtains. Definitely invest in a good quality dehumidifier and probably an oscilating fan to set in front of the game racks when the weather gets really warm and/or moist. All that might seem silly to some folks, but it sure beats having to replace a load of case covers or hunting down new carts because the contacts got all rusty and ruined.
