Right, and don't take it into the greenhouse until the little purple flowers are gone. It needs to be pollinated to actually make a fruit. Unless the nights start getting too cold, of course. Below 50 you'll have to bring it in. Don't forget it needs more water when the fruit is sizing up, too.
You're lucky the fruit will be forming inside the greenhouse, Anne. Here, my pineapples out in the garden get eaten by squirrels and raccoons before I can get to them. I have to spray them every day with a concoction of hot pepper stuff.