Do you mean Gaillardia? Gaillardia are perennial and will die down over winter, coming back in spring. I have mine in wide, shallow pots but am planning on putting them in the border next to the wall (dry) at some point over the next few months.

If you have a dryish border then that is the place to keep them - otherwise the greenhouse is perfect but do not feel that you need to.

Sadly, Kildermorie, I've never managed to get one through a winter - they always keel over here, not sure why, might be the soggy London clay.