I would only put it in the coop if there's a broody setting that you can put it under. You don't want the eggs to cool. The rooster is probably just curious.
Well, what you can do to make sure it's humid enough is put a damp washcloth over the eggs loosely. If it's not humid enough the chicks may not be able to get out of the shell and will eventually die. If you have a thermometer I would put that in there as close to the eggs as possible...