There is of course the famous proof that

Heaven is Hotter than Hell
[From Applied Optics vol. 11, (14) 1972]

         The temperature of Heaven can be rather accurately computed. Our authority is Isaiah 30:26,

                   "Moreover, the light of the Moon shall
                   be as the light of the Sun and the light
                   of the Sun shall be sevenfold, as the
                   light of seven days."

         Thus Heaven receives from the Moon as much radiation as we do from the Sun, and in addition 7*7 (49) times as much as the Earth does from the Sun, or 50 times in all. The light we receive from the Moon is one 1/10,000 of the light we receive from the Sun, so we can ignore that ... The radiation falling on Heaven will heat it to the point where i.e., Heaven loses 50 times as much heat as the Earth by radiation. Using the Stefan-Boltzmann
law for radiation, (H/E) temperature of the earth (-300K), gives H as 798K (525C). The exact temperature of Hell cannot be computed ...

       [However] Revelations 21:8 says

                   "But the fearful, and unbelieving ... shall
                   have their part in the lake which burneth
                   with fire and brimstone."

       A lake of molten brimstone means that its temperature must be at or below the boiling point, 444.6C. We have, then, that Heaven, at 525C is hotter than Hell at 445C.