  Spatially unresolved observations show that the cooling phase in solar flares
can be much longer than theoretical models predict. It has not yet been
determined whether this is also the case for different subregions within the
flare structure. We aim to investigate whether or not the cooling times, which
are observed separately in coronal loops and the supra-arcade fan (SAF), are in
accordance with the existing cooling models, and whether the temperature and
emission measure of supra-arcade downflows (SADs) are different from their
surroundings. We analysed the M5.6 limb flare on 13 January 2015 using SDO/AIA
observations. We applied a differential emission measure (DEM) reconstruction
code to derive spatially resolved temperature and emission measure maps, and
used the output to investigate the thermal evolution of coronal loops, the SAF,
and the SADs. In the event of 13 January 2015,the observed cooling times of the
loop arcade and the SAF are significantly longer than predicted by the Cargill
model, even with suppressed plasma heat conduction. The observed SADs show
different temperature characteristics, and in all cases a lower density than
their surroundings. In the limb flare event studied here, continuous heating
likely occurs in both loops and SAF during the gradual flare phase and leads to
an extended cooling phase.
