  In this paper, we compute the dimension of the Hochschild cohomology groups
of any $m$-cluster tilted algebra of type $\tilde{\mathbb{A}}$. Moreover, we
give conditions on the bounded quiver of an $m$-cluster tilted algebra
$\Lambda$ of type $\tilde{\mathbb{A}}$ such that the Gerstenhaber algebra
$\operatorname{HH}^*(\Lambda)$ has non-trivial multiplicative structures. We
also show that the derived class of gentle $m$-cluster tilted algebras is not
always completely determined by the Hochschild cohomology.
