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.