Richard J Kinch wrote:

The integrated temperature is still below zero even on a warm night.

What's an "integrated temperature"? :-)

What the radiation thermometer reads, looking at the background of outer
space, overlaid with a transparent but blackbody-radiating layer of
atmosphere...

Which absorbs IR...

The clear night sky is a cold window.

Clear skies are, but water vapor and clouds absorb IR. So do windows...

No, your understanding is naive.

Incorrect.

Nick