  We analyze the confinement/deconfinement transition of pure Yang-Mills
theories within the framework of the center-symmetric Landau gauge supplemented
by a Curci-Ferrari mass term that models the effect of the associated Gribov
copies in the infrared. In addition to providing details for earlier one-loop
calculations in that framework, we explore how the results depend on the
renormalization scale and/or on the renormalization scheme. We find that the
predicted values for the transition temperatures of SU($2$) and SU($3$)
Yang-Mills theories are similar in both schemes and are little sensitive to the
renormalization scale $\mu$ over a wide range of values including the standard
range $\smash{\mu\in[\pi T,4\pi T]}$. These values are also close both to those
obtained from a minimal sensitivity principle and to those of lattice
simulations, especially in the SU($3$) case. These results further confirm the
good behavior of perturbative calculations within the Curci-Ferrari model and
support the adequacy of the latter as an effective description of Yang-Mills
theories in the infrared. We perform a similar analysis for the spinodal
temperatures in the SU($3$) case and for the Polyakov loop, the order parameter
associated to the breaking of center symmetry.
