  Ever since their detection two decades ago, standing kink oscillations in
coronal loops have been extensively studied both observationally and
theoretically. Almost all driven coronal loop oscillations (e.g., by flares)
are observed to damp through time often with Gaussian or exponential profiles.
Intriguingly, however, it has been shown theoretically that the amplitudes of
some oscillations could be modified from Gaussian or exponential profiles if
cooling is present in the coronal loop systems. Indeed, in some cases the
oscillation amplitude can even increase through time. In this article, we
analyse a flare-driven coronal loop oscillation observed by the Solar Dynamics
Observatory's Atmospheric Imaging Assembly (SDO/AIA) in order to investigate
whether models of cooling can explain the amplitude profile of the oscillation
and whether hints of cooling can be found in the intensity evolution of several
SDO/AIA filters. During the oscillation of this loop system, the kink mode
amplitude appears to differ from a typical Gaussian or exponential profile with
some hints being present that the amplitude increases. The application of
cooling coronal loop modelling allowed us to estimate the density ratio between
the loop and the background plasma, with a ratio of between 2.05-2.35 being
returned. Overall, our results indicate that consideration of the thermal
evolution of coronal loop systems can allow us to better describe oscillations
in these structures and return more accurate estimates of the physical
properties of the loops (e.g., density, scale height, magnetic field strength).
