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. This type of thermometer is performing a digital numerical
integration as part of its analysis of the blackbody spectrum of the
target.

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. Ceramics emit radiation like anything
else. Nothing absorbs IR from the darkness of outer space, because there's
no IR to absorb. A room temperature skylight window is emitting IR, not
absorbing it, on a clear night.