  We present a new method for performing differential emission measure (DEM)
inversions on narrow-band EUV images from the Atmospheric Imaging Assembly
(AIA) onboard the Solar Dynamics Observatory (SDO). The method yields positive
definite DEM solutions by solving a linear program. This method has been
validated against a diverse set of thermal models of varying complexity and
realism. These include (1) idealized gaussian DEM distributions, (2) 3D models
of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a
non-linear force-free field, and (3) thermodynamic models from a
fully-compressible, 3D MHD simulation of AR corona formation following magnetic
flux emergence. We then present results from the application of the method to
AIA observations of Active Region 11158, comparing the region's thermal
structure on two successive solar rotations. Additionally, we show how the DEM
inversion method can be adapted to simultaneously invert AIA and XRT data, and
how supplementing AIA data with the latter improves the inversion result. The
speed of the method allows for routine production of DEM maps, thus
facilitating science studies that require tracking of the thermal structure of
the solar corona in time and space.
