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A unitary spinor transformation is used to show that the spin-down density of states (DOS) of half-metallic ferromagnets becomes nonzero at finite temperatures. In a strict sense, this thermally activated spin mixing means that half-metallic ferromagnetism is limited to zero temperature. Similar effects are created by crystal imperfections, interfaces, and surfaces. The calculations, which imply that the finite-temperature resistivity of an individual spin channel is never infinite, are used to discuss recent experimental work on half-metallic oxides and Heusler-type alloys.