  The problem of infrared divergence of the effective electromagnetic field at
finite temperature (T) is revisited. A model of single spatially localized
electron interacting with thermal photons is considered in the limit T to 0
using two different regularization schemes. The first is based on the shift i 0
to i varepsilon of the electron propagator pole in the complex energy plane,
and is used to explicitly calculate the effective field in the one-loop
approximation. We show that the matrix-valued imaginary part of the electron
self-energy can be consistently related to the pole shift, and that the
presence of the heat bath leads to appearance of an effective varepsilon sim T,
thus providing a natural infrared regulator of the theory. We find that the
one-loop effective Coulomb field calculated using this varepsilon vanishes. The
other scheme combines an infrared momentum cutoff with smearing of the
delta-functions in the interaction vertices. We prove that this regularization
admits factorization of the infrared contributions in multi-loop diagrams, and
sum the corresponding infinite series. The effective electromagnetic field is
found to vanish in this case too. An essentially perturbative nature of this
result is emphasized and discussed in connection with the long-range expansion
of the effective field.
