I'm not an archeologist, but I think most temples had walls. See this
plan of the Parthenon, for example, where dark black lines indicate walls, with entrances on the eastern and western sides. I'm not sure how integral the walls were for structural support, but temples (in the classical Greek world, anyway) were, practically speaking, repositories for dedicated items. Worship was not generally practiced inside the temples, but outside in the open air, at altars.