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The temperature dependence of the spin polarization of half-metallic ferromagnets is investigated by model calculations. Emphasis is on changes in the density of states, especially on the closure of the hybridization gap. The Stoner-type calculation yields a simple one-electron expression for the gap as a function of temperature and a corresponding transition temperature T*, above which the spin polarization is drastically reduced. The small parameter determining the finite-temperature breakdown of the spin splitting is the width of the hybridization gap relative to other bandwidth parameters. The model predictions are consistent with the experiment and with first-principles electronic structure calculations, and we argue that such band-structure effects are not limited to specific materials but rather widespread in hybridization-gap half-metals.