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According to the Wikipedia article, a non-mathematical explanation of Newton's Law of Cooling is: "The rate of heat loss of a body is proportional to the temperature difference between the body and its surroundings."

In other words, it is assumed that the rate of heat loss will increase linearly with temperature. This is basically correct if you consider only conduction; however, in the case of radiation, the radiation emitted by a body is proportional to the fourth power of the absolute temperature (for example, temperature measured in Kelvin). This will give you a curve, not a straight line; for small temperature intervals, you can approximate this with a straight line, but it will not be exact.

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