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Impacts on early Mars can produce H-2 and CH4 in the thermal plume. In a thick CO2 atmosphere, collision-induced absorptions between CO2-H-2 and CO2-CH4 can boost the greenhouse effect. We construct a simple model of the impact history of Mars and show that for a variety of impactor types and CO2 surface pressures >0.5 bars, postimpact surface temperatures due to H-2 alone can exceed the melting point of water for much longer periods of time than from the dissipation of the heat derived from the impactor's kinetic energy. This longer timescale is set by hydrogen escape rather than radiation to space. Cumulatively, the Noachian surface may have been above the melting point of water for millions of years by this mechanism. These greatly extended postimpact warm environments may have played a larger role in the erosion and mineralogy of the surface than previously thought and may partly explain some of the observed fluvial features.