In Applied Optics (1972, 11 A14) there appeared a calculation of the respective temperatures of Heaven and Hell. That of Heaven was computed by substituting the values given in Isaiah 30 26  in the Stefan-Boltzman radiation law, so that (H/E)4 = 50, where E, the absolute temperature of the Earth, is 300ºK, whence the temperature of Heaven, H, is 798ºK or 525ºC. This is hard to find fault with.
The assessment of the temperature of Hell stands, I suggest, on less firm ground. As authority we use the data provided in Revelations 21 8 , so that the temperature of Hell seems to be 444.6ºC–the temperature at which liquid sulfur is in equilibrium with its vapour–a temperature indeed which is sufficiently reliable to be used in the secondary calibration of pyrometers.
Now this last reckoning fails to follow the argument through. 444.6ºC is the temperature at which liquid sulfur is in equilibrium with its vapour at normal atmospheric pressure. Have we any data as to the pressure likely to be found in Hell?
The answer is “Yes”. A nineteenth century mathematician has already provided the groundwork for us  and we may feel confident that by the year 2000 the total number of the damned will be at least 29,422,641,251,519,917,000 souls. Yet the area of the valley of Gehinnom  is only 7,000,000 square meters.
We can now apply these figures in the Ideal Gas Equation to calculate what the pressure will be in the valley of Gehinnom. Since surely some souls must have been damned since 1877 , the pressure can only have increased since these calculations were made and the equilibrium point on the phase diagram of sulfur must have shifted still further, so that if we can show that at a temperature of 525ºC sulfur would still be liquid at the pressure calculated (which is a minimum value, remember), Hell (Gehinnom) is now cooler than Heaven.
Certain corrections must be applied first, however.
1. Neiht based his calculation on a date of creation of 1658 + 2326 – 1877 = 2107 BC (minimum). Counting generations in the Bible gives a date for the Creation of 4004 BC. However, atomic dating has shown that Olduvai man is at least 2 × 106 years old .
2. We should use a Fibonacci series for the expansion, not a simple doubling series.  The ancient Jewish laws against inbreeding also act in the same direction. 
3. By a fortunate coincidence, the effects of 1 and 2 cancel each other exactly. 
4. The human body is not an ideal gas, but
5. A good deal of it is gaseous at 525ºC, and in any case,
6. It could well be that at very great pressures the external pressure may well exceed the pressure of electromagnetic repulsion, when different “gas” laws would apply. This merely explains how the Lord works in fitting so large a number of damned souls into so small a space  and it need not be quantitative.
In the calculation the following assumptions are made:
1. The average height can be taken as one meter. This seems a fair figure between the newborn babe and the fullgrown man.
2. The average space needed is about 30 cm × 20 cm. It seems unlikely that any closer packing could be achieved. Neiht uses a figure of 1/20 cubic meters per person, which is nearly identical with my independent assessment. Mine allows a neat cancellation, later.
3. I have assumed that not more than two layers of damned persons can be accommodated, since otherwise those in the middle layers would escape the full rigours of Hell.
The volume available in Gehenna is 60 × 106 × 2 m3 and
The original volume of the damned is 0.06 × 29.422641 × 1018m3
Then, at constant temperature (which we assume, taking equilibrium)
P1V1 = P2V2 or P2 = P1V1/V2
P2 = [29 × 6 × 1016] / [2 × 6 × 107] = 14.5 × 109 atmospheres
Now let us see what pressure is needed to liquefy sulfur vapour at 525ºC.
We have, using the Clausius-Cleypeyron equation in its integrated form,
Log P = 7.43287 – 3268.2 / T
where P = pressure in mm Hg
and T = the elevated boiling point in ºK,
Log P = 7.43287 – (3268.2/798) = 3.3373813
P = 2174.607 mm Hg = 2.86 atmospheres
(1) is so much greater than (2) that Revelations 21 8 indicates a temperature very considerably higher than 525ºC.
Thus, Hell is hotter than Heaven (which remains deucedly hot).
Author: Dr. Tim Healey, F. R. C. R.; M. I. Nuc. E. Published in The Journal of Irreproducible Results (1979)