Suppose Earth has drifted away from solar system for some reason. It has been 320 years since drifting started. For almost 250 years, it is farther away from Neptune. - How cold would the surface temperature be? - Would it effect the inner temperature? (The "1 degrees centigrade per 33 meters" principle)
There's a sketch of an answer here
Basically, at 320 years, there hasn't been time to freeze the planet properly. The oceans won't be frozen solid yet, and I suspect that the atmosphere would not be raining out yet. Based on borehole climatology, I'd guesstimate that you'd need to be perhaps 100-200 meters down to be able to ignore it, at this stage.
The gradual progression of ocean freezing, the need to go deeper and the freeze-out of the atmosphere would all be interesting, though.