From what I recall, a tidelocked world with an atmosphere would theoretically be habitable, but only along a strip near the hot side of the terminator.
Yes, and the rules in WBH provide for that. The problem I had was that the ensuing equations for determining the sub-solar and anti-solar extremes made for such dramatic differences that I couldn't see how the planet would maintain a stable atmosphere or even hydrosphere. With temps on the sub-solar side well above the boiling point of water and below the freezing point of most gasses on the anti-solar side, I couldn't see how it would last.
If you're looking for a formula however, have you looked at this
No, I hadn't. Thank you! That gave me good numbers for the sub-solar, but still didn't convince me that an atmosphere could still exist under those extremes.
It might be that tide-locked worlds are atmospherically unstable and will be completely destroyed in a certain multiple of thousands of years (dependent upon mass). In order for them to be stable, there must be a significant warming effect due to hot winds blowing in from the dayside to offset the extreme cold of the nightside. If this is going to work in game terms (reality may eventually say, "No, not possible.") for me, I'm going to need some thermal moderation factor to plug in.