Cooling a hot gold foil in space Suppose in a space-ship there is a hot (600K) gold foil a few atoms thin and that it is thrown out in space (4K): how long would it take for the foil's temp to drop to 200K or 10K?
Is there a formula? Naively one would think that it should take a couple of seconds for atoms to stop oscillating and that after the first second there would be a drastic drop in frequency, is that so or is the drop smooth and slow?
In the chemistry site a found an answer where, talking of diatomic molecules, they state that it takes hours:

If these molecules are in equilibrium with surrounding then these
  surroundings must also emit/absorb radiation to keep the total energy
  constant. If you were to suddenly isolate your block of (heteronuclear
  diatomic) molecules, say in space, then the radiation emitted would
  over a few hours remove energy so that the molecules will end up in
  their zero point levels.

is that true only when many molecules/atoms are grouped together? what happens when a foil is only a few atoms thick?
 A: The loss of energy from the gold foil will be by radiation and proportional to $T^4 - 4^4$ where $T$ is the temperature of the foil.
So the rate at which the foil loses energy depends on the temperature of the foil.
You need to look up the Stefan_Boltzmann Law to find the constant of proportionality.
The other parameter that need is the specific heat capacity of gold which is a function of temperature.
On pages 38 to 39 in this publication you will find tabulated the specific heat capacity of gold as a function of temperature.  
You then have rate of heat loss from the gold foil = mass of gold foil $\times$ specific heat capacity of gold foil $\times$  rate of change of temperature with time.
Combining this equation with Stephan_Boltzmann will give you an equation for the rate of change of temperature of the gold foil.
You will then have to do an integration having found functional relationships between the specific heat of gold and temperature.
Down to about $170 \rm K$ the specific heat capacity of gold can be assumed to be sensibly constant and below that temperature and then a polynomial fit (cubic?) will enable you to estimate time for the cooling.
