One of the defining characteristics of a solar flare is the impulsive formation of very high temperature plasma. The properties of the thermal emission are not well understood, however, and the analysis of solar flare observations is often predicated on the assumption that the flare plasma is isothermal. The EUV Variability Experiment (EVE) on the Solar Dynamics Observatory provides spectrally resolved observations of emission lines that span a wide range of temperatures (e.g., Fe XV-Fe XXIV) and allow for thermal flare plasma to be studied in detail. In this paper we describe a method for computing the differential emission measure distribution in a flare using EVE observations and apply it to several representative events. We find that in all phases of the flare the differential emission measure distribution is broad. Comparisons of EVE spectra with calculations based on parameters derived from the Geostationary Operational Environmental Satellites soft X-ray fluxes indicate that the isothermal approximation is generally a poor representation of the thermal structure of a flare.