According to James Stewart's Calculus book (exercise 14, page 609),
Newton’s Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large.
In general, I've read about this law in the context of differential equations where little information is given (because the focus is the math and not the physics). So, I'd like to know:
What sort of experiments was done to establish this law as a scientific truth? How can we justify that this law is valid?
(If this question is not appropriate for the site, let me know and I will delete it.)