  Flare emissions in X-ray and EUV wavelengths have previously been modeled as
the plasma response to impulsive heating from magnetic reconnection. Some
flares exhibit gradually evolving X-ray and EUV light curves, which are
believed to result from superposition of an extended sequence of impulsive
heating events occurring in different adjacent loops or even unresolved threads
within each loop. In this paper, we apply this approach to a long duration
two-ribbon flare SOL2011-09-13T22 observed by the Atmosphere Imaging Assembly
(AIA). We find that to reconcile with observed signatures of flare emission in
multiple EUV wavelengths, each thread should be heated in two phases, an
intense impulsive heating followed by a gradual, low-rate heating tail that is
attenuated over 20-30 minutes. Each AIA resolved single loop may be composed of
several such threads. The two-phase heating scenario is supported by modeling
with both a zero-dimensional and a 1D hydrodynamic code. We discuss viable
physical mechanisms for the two-phase heating in a post-reconnection thread.
