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 $sim 2times 10^{-5}$, a total dust mass of $sim 2times 10^9,{rm M_odot}$, and a dust mass fraction of $sim 3times 10^{-6}$. 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.
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