Up to a point. It's not that the air needs to be cold, it's that it needs to be cooler near the ground than above it. Sound travels faster in the hotter air, and sound waves curve and refract from the zone of higher speed into the zone of lower speed.

So in the night, when the air gets colder, the sound from up above tends to curve towards the ground and propagate farther. During the day is the other way round. More to read: https://blog.thermaxxjackets.com/refraction-of-sound-waves-acoustic-shadows-explained