From what I remember, most (all?) of the heat in the atmosphere, or at least in the troposphere, comes from the ground, with convection carrying heat into the upper atmosphere.
Looking at my temperature graph from my weather station in my backyard, overnight the temp dropped about 1 Freedom Unit per hour. So at the absolute quickest, and assuming an average surface temperature of 60 F when the sun vanishes, here’s what I have
| Atmospheric gas | melting point (F) | hours until gas begins condensing | days until gas begins condensing |
|---|---|---|---|
| water | 32 | 28 | 1.166666667 |
| CO2 | -70 | 130 | 5.416666667 |
| argon | -307 | 367 | 15.29166667 |
| N2 | -346 | 406 | 16.91666667 |
| O2 | -361 | 421 | 17.54166667 |
This is likely way too fast, as I believe the colder you are, the less heat you lose. Also, melting/boiling points depend on the surrounding pressure, which will get effected by the other gases precipitating. 70 below isn’t unheard of, and the coldest temp ever reached was -128 in Antarctica.
What do you think. IDK I’m le tired.
A Deepness in the Sky, by Vernor Vinge, explores this question with a star that goes dark every 50 years. Seems like it would depend upon the planetary specifics, i.e. atmosphere composition and volcanic activity. You could have a great telescope afterwards.