The best way to store fondant cake overnight is to cover the fondant cake with some plastic wrap or use a cake storage container with a lid.
Then just leave the fondant cake out at room temperature overnight and the fondant cake will be okay at room temperature overnight.
Actually fondant cake will last at room temperature for up to 3 days as long as you keep it covered or sealed in some plastic wrap.
If it's hot in your kitchen it would be best to keep the fondant cake refrigerated while still being either in the cake storage container or wrapped in some plastic wrap.