  We study the thermalization of an elementary quantum system modeled by a
two-level atom interacting with stationary electromagnetic fields out of
thermal equilibrium near a dielectric slab. The slab is held at a temperature
different from that of the region where the atom is located. We find that when
the slab is a nonabsorbing and nondispersive dielectric of a finite thickness $
d$, no out of thermal equilibrium effects appear as far as the thermalization
of the atom is concerned, and a finite thick dielectric slab with a tiny
imaginary part in the relative permittivity $\operatorname{Im} \epsilon$
behaves like a half space dielectric substrate if $\frac{\operatorname{Im}
\epsilon}{\sqrt{\operatorname{Re}\epsilon-1}} \frac{d}{\lambda_0} > 1$ is
satisfied, where $\lambda_0$ is the transition wavelength of the atom. This
condition can serve as a guide for an experimental verification, using a
dielectric substrate of a finite thickness, of the effects that arise from out
of thermal equilibrium fluctuations with a half-space (infinite thickness)
dielectric.
