I think an important factor must be that it takes a lot of energy for water to change from solid to liquid form. So the heat raises the temperature of the wall to the melting point, but then it will actually take a while to accumulate enough heat to make it a liquid. But at the same time, heat will slowly dissipate, keeping the wall solid at melting point.
Hence it can be 15 degrees below freezing outside and 15 degrees above freezing inside… and the walls stay at melting point.
Please correct me if I am wrong!
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