A Chern–Weil formula for the Chern character of a perfect curved module

Let $k$ be a field of characteristic 0 and $\mathcal{A}$ a curved $k$-algebra. We obtain a Chern–Weil-type formula for the Chern character of a perfect $\mathcal{A}$-module taking values in $HN^{II}_0(\mathcal{A})$, the negative cyclic homology of the second kind associated to $\mathcal{A}$, when $\mathcal{A}$ satisfies a certain smoothness condition.