  The internal heat loss, or cooling, of a planet determines its structure and
evolution. We study the effects of irradiation, metallicity of the atmosphere,
heat redistribution, stratospheres, and the depth where the heat redistribution
takes place on the atmospheric structure, the core entropy, and subsequently on
the cooling of the interior of the planet. We address in a consistent fashion
the coupling between the day and the night sides of a planet by means of model
atmosphere calculations with heat redistribution. We assume that strong
convection leads to the same entropy on the day and night sides and that
gravity is the same on both hemispheres. We argue that the core cooling rates
from the two hemispheres of a strongly irradiated planet may not be the same
and that the difference depends on several important parameters. If the
day-night heat redistribution is very efficient or if it takes place at the
large optical depth, then the day-side and the night-side cooling may be
comparable. However, if the day-night heat transport is not efficient or if it
takes place at a shallow optical depth then there can be a large difference
between the day- and the night-side cooling and the night side will cool more
efficiently. If stellar irradiation becomes stronger, e.g. owing to stellar
evolution or migration, cooling from both the day and the night sides is
reduced. Enhanced metallicity of the atmosphere would act as an added "blanket"
and reduces both the day- and the night-side cooling. However, a stratosphere
on the planetary day side can enhance day-side cooling since its opacity acts
as a "sunshade" that screens the stellar irradiation. These effects may also
influence the well-known gravity darkening and bolometric albedo effects in
interacting binaries, especially for strongly irradiated cold components.
