Context. 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.
Aims: 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.
Methods: 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.
Results: 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.
Conclusions: 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.