Daily differential emission measure (DEM) distributions of the solar corona are derived from spectra obtained by the Extreme-ultraviolet Variability Experiment (EVE) over a 4-year period starting in 2010 near solar minimum and continuing through the maximum of solar cycle 24. The DEMs are calculated using six strong emission features dominated by Fe lines of charge states VIII, IX, XI, XII, XIV, and XVI that sample the non-flaring coronal temperature range 0.3--5 MK. A proxy for the non-XVIII emission in the wavelength band around the 93.9 AA line is demonstrated. There is little variability in the cool component of the corona (T $<$ 1.3 MK) over the four years, suggesting that the quiet-Sun corona does not respond strongly to the solar cycle, whereas the hotter component (T $>$ 2.0 MK) varies by more than an order of magnitude. A discontinuity in the behavior of coronal diagnostics in 2011 February--March, around the time of the first X-class flare of cycle 24, suggests fundamentally different behavior in the corona under solar minimum and maximum conditions. This global state transition occurs over a period of several months. The DEMs are used to estimate the thermal energy of the visible solar corona (of order $10^{31}$ erg), its radiative energy loss rate (2.5--8 $times 10^{27}$ erg s$^{-1}$), and the corresponding energy turnover timescale (about an hour). The uncertainties associated with the DEMs and these derived values are mostly due to the coronal Fe abundance and density and the CHIANTI atomic line database.
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