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You left out that the glass has to be colder than the ambient air temperature for that to happen. Same with the safe. It's the air at the chilled surface being cooled below its dew point (>100% RH) that causes it to be unable to keep all the water vapor in it dissolved. This is why the Goldenrod type heaters work.
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Yep, and considering normal room thermal cycles such as:
1) sunlight from a window in the daytime.
2) Safe sitting on a cold floor.
3) External heat sources (space heater and room vents)
Internal heat in the safe is a good idea.