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Winds and temperature

I hear frequently on weather reports comments along the lines of "little
wind tonight so expect temperatures to drop". I haven't managed to
convince myself of the reason for this, so I asked around - some I have

1) It's geographic. Our winds are warmer than our existing air (unlikely)

2) Air can radiate energy outward more efficiently when it isn't moving
(just doesn't make sense)

3) Cold air sinks and without winds to remix it, the air near the ground
gets colder.
(Does that mean that the air aloft is warmer on still nights than on windy

4) It's an energy consideration; the pressure gradient does work on the
air and that raises its temperature (hmm ...)

5) It's an energy consideration; frictional effects of air resistance lead
to increased temperatures.
(But this shouldn't apply in flat undeveloped areas where frictional
effects are much lower)

6) It's not real. Still nights are often cloudless and it's the lack of
clouds that causes the temperature drop.
(This seems reasonable, but then why the emphasis placed on winds?)

Anyone out there got the correct answer?