  We study, by means of numerical lattice simulations, the properties of the
reconfinement phase transition taking place in trace deformed $SU(3)$
Yang-Mills theory defined on $\mathbb{R}^3\times S^1$, in which center symmetry
is recovered even for small compactification radii. We show, by means of a
finite size scaling analysis, that the reconfinement phase transition is
first-order, like the usual $SU(3)$ thermal phase transition. We then
investigate two different physical phenomena, which are known to characterize
the standard confinement/deconfinement phase transition, namely the
condensation of thermal magnetic monopoles and the change in the localization
properties of the eigenmodes of the Dirac operator. Regarding the latter, we
show that the mobility edge signalling the Anderson-like transition in the
Dirac spectrum vanishes as one enters the reconfined phase, as it happens in
the standard confined phase. Thermal monopoles, instead, show a peculiar
behavior: their density decreases going through reconfinement, at odds with the
standard thermal theory; nonetheless, they condense at reconfinement, like at
the usual confinement transition. The coincidence of monopole condensation and
Dirac mode delocalization, even in a framework different from that of the
standard confinement transition, suggests the existence of a strict link
between them.
