No. This is not why this time and day of the lunar cycle was chosen. It was chosen because, with the sun low on the horizon (10 to 15°) , the sun cast long, sharp shadows which helped Armstrong see lunar surface terrain such as craters and rocks, to enable him to find and land at a safe site at the Sea of Tranquility.
You do know that this refers to surface temperature, don't you? Not "air" temperature?
Irrelevant, since A11 astronauts were never on the moon surface at "night time" - even if the sky was black.
During Apollo 11, the surface temperature was between -23°C and 7°C (-9°F and 45°F). Not that extreme.
Not that surface, or event ambient, temperature has anything to do with taking a photo of the lunar day time sky . . .