  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.
