The recent analysis of observations taken with the EIS instrument on Hinode suggests that well constrained measurements of the temperature distribution in solar active regions can finally be made. Such measurements are critical for constraining theories of coronal heating. Past analysis, however, has suffered from limited sample sizes and large uncertainties at temperatures between 5 and 10 MK. Here we present a systematic study of the differential emission cores. We focus on measurements in the inter-moss region, that is, the region between the loop footpoints, where the observations are easier to interpret. To reduce the uncertainties at the highest temperatures we present a new method for isolating the Fe XVIII emission in the AIA/SDO 94 channel. The resulting differential emission measure distributions confirm our previous analysis showing that the temperature distribution in an active region core is often strongly peaked near 4 MK. We characterize the properties of the emission distribution as a function of the total unsigned magnetic flux. We find that the amount of high temperature emission in the active region core is correlated with the total unsigned magnetic flux, while the emission at lower temperatures, in contrast, is inversely related. These results provide compelling evidence that high temperature active region emission is often close to equilibrium, although weaker active regions may be dominated by evolving million degree loops in the core.
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