There could be moons as big as Titan, or even bigger than Ganymede that are as far as Jupiter or Saturn from their star. These moon do not get that much energy from their star.They actually get it from a Jupiter or Saturn size planet.
A great example of such a phenomenon is the relationship between Io and Jupiter. Io is as hot as Venus because Io is not in the habitable zone of its planet, whereas Europa is.
The pull betweenJupiter and its moons causes Io to be volcanic.
A bigger moon, similar to Io, could exist and have an atmosphere. The atmosphere would also have its own warm zone like earth does. You can tell by earths mountains that there is a snow level on top of the mountains.
And Io like moon with and think atmosphere like titan would could have flying life. The surface could be un stable but the upper part of the atmosphere could have the right temputure where you could breath.
If Io had a thicker atmosphere it could have had or have life.
Problems:
The moon could have a volcanic surface where you you could have a lot or rain hitting the surface area. It could cause the moon to cool. It might cause it cool to much untill the atmosphere could get weaker because the moon Tidal fictioning is getting weak.
This could make the surface the right temputure for planet life to be on but this is only tempurary for 100's of years
First about 500 years the sky will get very cloudy because the atmosphere is mixing up tidal fiction and coolness of space.
This will cause the atmosphere to cool down because the tidal heating is making the atmosphere spread out into space.
This could leave a giant areless moon in space.
Any life that was on that moon was their for only 100 years
If the moon is as far as Neptune from it's star.This could cause the process to go even quicker.
If the moon was the size of a super earth this could cause the moon to enter a diffrent stage that could cause the moon to go the opposite way and become an ice giant or gas giant
Possiblities:
The moon could replinish itsself and be about the right size to keep and atmosphere going with out the atmosphere drifting away or it being a Ice Giant