What you are experiencing is the dew point reaching the ambient temperature.
This is a view for my weather station for the last 24 hours. You can see around 6 AM, the dew point and the outdoor temperature get real close.
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If we look at humidity level, we can see that around 6 AM, it was near 100%.
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Hotter air can hold more water than colder water. A 50% humidity at 5° C have much less water in suspension than air at 30° C with still 50% humidity. Actually the % of humidity is the % of the maximum amount of water you can hold in the air.
I live in a colder climate and we experience the opposite in winter. The cold air from outside get in our house, and because very dry after being heated to indoor temperature. That make the air very dry and uncomfortable. We actually have to run humidifier to keep it bearable.
So again, what you experience is the air no longer being able to hold all the water it have in it. The water have to condensate somewhere and it do not matter if the temperature is hotter/colder, the water just have to go somewhere. In that case a larger radiator would indeed provide more surface for condensation. But that is not because it's colder than air. That is just impossible without something that would actively cool the water.
Also, all this assume you have no air conditioning and you open your windows to cool your house at night. If you have an air conditioner, the temperature will be stable and it will remove humidity from the air anyway.