  We compute the finite temperature ghost and gluon propagators of Yang-Mills
theory in the Landau-DeWitt gauge. The background field that enters the
definition of the latter is intimately related with the (gauge-invariant)
Polyakov loop and serves as an equivalent order parameter for the deconfinement
transition. We use an effective gauge-fixed description where the
nonperturbative infrared dynamics of the theory is parametrized by a gluon mass
which, as argued elsewhere, may originate from the Gribov ambiguity. In this
scheme, one can perform consistent perturbative calculations down to infrared
momenta, which have been shown to correctly describe the phase diagram of
Yang-Mills theories in four dimensions as well as the zero-temperature
correlators computed in lattice simulations. In this article, we provide the
one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon
propagators for a large class of gauge groups and present explicit results for
the SU(2) case. These are substantially different from those previously
obtained in the Landau gauge, which corresponds to a vanishing background
field. The nonanalyticity of the order parameter across the transition is
directly imprinted onto the propagators in the various color modes. In the
SU(2) case, this leads, for instance, to a cusp in the electric and magnetic
gluon susceptibilities as well as similar signatures in the ghost sector. We
mention the possibility that such distinctive features of the transition could
be measured in lattice simulations in the background field gauge studied here.
