  Simulating the dust content of galaxies and their surrounding gas is
challenging due to the wide range of physical processes affecting the dust
evolution. Here we present cosmological hydrodynamical simulations of a cluster
of galaxies, $M_\text{200,crit}=6 \times 10^{14}\,{\rm M_\odot}$, including a
novel dust model for the moving mesh code {\sc Arepo}. This model includes dust
production, growth, supernova-shock-driven destruction, ion-collision-driven
thermal sputtering, and high temperature dust cooling through far infrared
re-radiation of collisionally deposited electron energies. Adopting a rather
low thermal sputtering rate, we find, consistent with observations, a
present-day overall dust-to-gas ratio of $\sim 2\times 10^{-5}$, a total dust
mass of $\sim 2\times 10^9\,{\rm M_\odot}$, and a dust mass fraction of $\sim
3\times 10^{-6}$. The typical thermal sputtering timescales within $\sim
100\,{\rm kpc}$ are around $\sim 10\,{\rm Myr}$, and increase towards the outer
parts of the cluster to $\sim 10^3\,{\rm Myr}$ at a cluster-centric distance of
$1\,{\rm Mpc}$. The condensation of gas phase metals into dust grains reduces
high temperature metal-line cooling, but also leads to additional dust infrared
cooling. The additional infrared cooling changes the overall cooling rate in
the outer parts of the cluster, beyond $\sim 1\,{\rm Mpc}$, by factors of a
few. This results in noticeable changes of the entropy, temperature, and
density profiles of cluster gas once dust formation is included. The emitted
dust infrared emission due to dust cooling is consistent with observational
constraints.
