A wheat variety designated W000582Z2, the plants and seeds of wheat variety W000582Z2, methods for producing a wheat plant produced by crossing the variety W000582Z2 with another wheat plant, and hybrid wheat seeds and plants produced by crossing the variety W000582Z2 with another wheat line or plant, and the creation of variants by mutagenesis or transformation of variety W000582Z2. This invention also relates to methods for producing other wheat varieties or breeding lines derived from wheat variety W000582Z2 and to wheat varieties or breeding lines produced by those methods.