  We make a generic remark on thermal history of a single brane cosmology in
models with an infinitely large single extra dimension. We point out that the
reheat temperature of the Universe is bounded by an excess production of
gravitons from the thermal bath. The actual bound is given by the brane
tension. If the initial temperature of the Universe is larger than this bound,
then an efficient graviton production shall prevail. However, the brane cools
down gradually as the Kaluza-Klein gravitons take the energy in excess away
from the brane. The cooling continues until the radiation dominated phase is
restored, which occurs before the Big Bang Nucleosynthesis. We argue whatsoever
be the early evolution of the Universe, the final radiation dominated phase
always starts after the Universe transits from non-conventional era to the
standard cosmological era.
