Outflowing winds of multiphase plasma have been proposed to regulate the buildup of galaxies, but key aspects of these outflows have not been probed with observations. By using ultraviolet absorption spectroscopy, we show that "warm-hot" plasma at 10(5.5) kelvin contains 10 to 150 times more mass than the cold gas in a post-starburst galaxy wind. This wind extends to distances > 68 kiloparsecs, and at least some portion of it will escape. Moreover, the kinematical correlation of the cold and warm-hot phases indicates that the warm-hot plasma is related to the interaction of the cold matter with a hotter (unseen) phase at >>10(6) kelvin. Such multiphase winds can remove substantial masses and alter the evolution of post-starburst galaxies.