Sun-as-a-star EUV spectroscopy from EVE (the Extreme-ultraviolet Variability Experiment, on board the Solar Dynamics Observatory) frequently shows striking irradiance reductions following major solar flares. These coincide with dimming events as seen in EUV and X-ray images, involving the evacuation of large volumes of the corona by the associated coronal mass ejections. The EVE view of the dimming process is precise and quantitative, whereas difference imaging in the EUV reveals the structures to be full of complicated detail due most likely to unrelated activity.We have studied a sample of 11 events, mostly GOES X-class flares, all of which were associated with coronal mass ejections. For a set of 9 lines of Fe ions at stages VIII - XIII, corresponding to nominal peak formation temperatures below log(T) = 6.3, we have compared the emission-measure-weighted temperatures of the dimming mass and the preflare global corona. We find similar temperatures by this measure, but with a distinctly narrower variation in the preflare samples. For higher ionization states weak emission commonly appears during the dimming intervals, consistent with residual late-phase flare late-phase development. The dimming depths do not appear to correlate with the preflare state of the global corona.