  In this paper we study, by means of numerical simulations, the topological
properties of $SU(3)$ and $SU(4)$ trace deformed Yang-Mills theory defined on $
\mathbb{R}^3\times S^1$, in which center symmetry is recovered even at small
compactification radii. In particular, we compute the topological
suscpetibility $\chi$ and the coefficient $b_2$ (related to the fourth cumulant
of the topological charge distribution). We find that these observables
computed in the deformed theory when center symmetry is recovered are
compatible with their values at zero temperature both for 3 and 4 colours
