I recently came across an article in Wikipedia, which claimed that medieval civilizations used to leave water out overnight in an insulated pot during clear and calm nights, which results in the water radiating away its heat and freezing into ice. Note that this method does not require the ambient atmospheric temperature to be below the freezing level.
Which brings me to my question: How is this possible, and what is the lowest temperature one can hope to cool a well insulated object during night? Let us assume, for instance, that it is a calm night where the ambient temperature of the atmosphere is 15C. While the object radiates its heat out to space, the atmosphere also radiates heat into the object (since we hope to cool the object to below the ambient temperature). How can this be calculated, ie., what is the 'radiative' temperature of the night sky, instead of the ambient temperature?