  We test the compatibility and biases of multi-thermal flare DEM (differential
emission measure) peak temperatures determined with AIA with those determined
by GOES and RHESSI using the isothermal assumption. In a set of 149 M- and
X-class flares observed during the first two years of the SDO mission, AIA
finds DEM peak temperatures at the time of the peak GOES 1-8 A flux to have an
average of Tp = 12.0+/-2.9 MK and Gaussian DEM widths of log10(sigma_T) =
0.50+/-0.13. From GOES observations of the same 149 events, a mean temperature
of Tp = 15.6+/-2.4 MK is inferred, which is systematically higher by a factor
of TGOES/TAIA = 1.4+/-0.4. We demonstrate that this discrepancy results from
the isothermal assumption in the inversion of the GOES filter ratio. From
isothermal fits to photon spectra at energies of E ~ 6-12 keV of 61 of these
events, RHESSI finds the temperature to be higher still by a factor of
TRHESSI/TAIA = 1.9+/-1.0. We find that this is partly a consequence of the
isothermal assumption. However, RHESSI is not sensitive to the low-temperature
range of the DEM peak, and thus RHESSI samples only the high-temperature tail
of the DEM function. This can also contribute to the discrepancy between AIA
and RHESSI temperatures. The higher flare temperatures found by GOES and RHESSI
imply correspondingly lower emission measures. We conclude that self-consistent
flare DEM temperatures and emission measures require simultaneous fitting of
EUV (AIA) and soft X-ray (GOES and RHESSI) fluxes.
