How close to a host star can a tidally locked planet be and its dark side still maintain a moderate temperature? So, imagine an atmosphere-less planet, tidally locked to a sun-like star. How close to the star can the planet be before its dark side becomes too hot?
I imagine that at some point the rocks on its sunlit side will melt and evaporate so that the dark side would experience rocky precipitation. Would this be true?
Also, at some point the atmosphere of the star itself would engulf the planet.
But at which point would these effects make the conditions on the dark side unbearable?
Your general idea about this process is correct. At close semimajor axis distance, rock can evaporate and will form a Silicate-oxygen atmosphere.
For low-mass rocky planets, the condensation flow from day to night-side, as it necessarily is very hot, will have to compete with the possibility of instead escaping vertically from the nightside, instead of precipitating. For higher-mass planets, vertical escape will be too difficult, and the hot Silicate-Oxygen gas will recondense on the nightside and therefore heat via thermal radiation and condensation latent heat.
This is a problem on which current research is in progress, and not many groups have worked on this, with the exception of one fantastic article that came out this year. They glue four different 1-D models together to represent vertical and horizontal for each day and night-side of catastrophically evaporating planets together, in order to create a sort of fake-2D model of the planetary Silicate-atmosphere.
Their nightsides are very hot in general (500-1000K), but they sadly do not give silicate densities or pressures. Hence, without the density, it is difficult to estimate how much the heat transfer between the Silicate gas and a human would be, i.e. how much a human would 'feel'.
If you are very curious though, I am sure you can construct this effect, by assuming Silicate saturation pressures, which are given in this article.