The problem of estimating the thermal corrections to Casimir
and Casimir-Polder interactions in systems involving conducting
plates has attracted considerable attention in the recent
literature on dispersion forces. Alternative theoretical
models, based on distinct low-frequency extrapolations of the
plates reflection coefficient for transverse electric (TE)
modes, provide widely different predictions for the magnitude
of this correction. In this paper we examine the most widely
used prescriptions for this reflection coefficient from the
point of view of their consistency with the Bohr-van Leeuwen
theorem of classical statistical physics, stating that at
thermal equilibrium transverse electromagnetic fields decouple
from matter in the classical limit. We find that the theorem is
satisfied if and only if the TE reflection coefficient vanishes
at zero frequency in the classical limit. This criterion
appears to rule out some of the models that have been
considered recently for describing the thermal correction to
the Casimir pressure with non-magnetic metallic plates.