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There is the famous saying about a frog that is put in water that are slowly boiling will not jump out until it's too late. I realize it happens because of the frog's cold blood that adjusts to the temperature change until it's too late. Will this work as well on an animal with warm blood, or will the animal jump out ones it gets hot, but not hot enough to cause permanent damage?
Edit due to comments:
Cold blooded animals, like the frog, can adjust easier to their surrounding when the surrounding changes temperature gradually as their body temperature adjusts with the surroundings. Will the same happen to a warm bodied creature, and will it find it easier to adjust to the surrounding if the change is gradual.
For example, I don't like saunas, when I get in them I have problem breathing and I can't stand the heat, which means that I can be in a sauna for a very short time until I have had enough and get out. Will putting me in a sauna at room temperature and then turning it on to gradually begin to heat until its destination temperature will allow me to fill more comfortable and stay longer inside once it's at the normal sauna temperature?
This answer belongs on Skeptics. Sorry to disappoint, but the "boiled frog" phenomenon is an "old folk warning". This essentially negates your original question altogether. Neither a cold-blooded animal (such as a frog) or warm-blooded animal will boil to death under the conditions implied by the warning (i.e. escape is permitted and water is heated very gradually).
1897 research by German scientist E. W. Scripture, upon which the fable may have first been based, has been deemed flawed by scientists:
From Scripture's research: “… a live frog can actually be boiled without a movement if the water is heated slowly enough; in one experiment, the temperature was raised at the rate of 0.002 degrees Celsius per second, and the frog was found dead at the end of 2.5 hours without having moved."
According to Dr. Karl S. Kruszelnicki (Australian scientist): "[T]he numbers just don't seem right. If the water comes to a boil, that means a final temperature of 100 degrees Celsius. In that case, the frog would have to have been put into the water at 82 degrees Celsius. Surely, the frog would have died immediately."
According to Dr. Victor H. Hutchinson (Herpetologist and Zoology Professor at University of Oklahoma): "The legend is entirely incorrect! The 'critical thermal maxima' of many species of frogs have been determined by several investigators. In this procedure, the water in which a frog is submerged is heated gradually at about 2 degrees Fahrenheit per minute. As the temperature of the water is gradually increased, the frog will eventually become more and more active in attempts to escape the heated water. If the container size and opening allow the frog to jump out, it will do so."
Whit Gibbons (University of Georgia) says that there is an important message behind the false legend:
So where does that leave us with the boiling frog as a metaphor for the human response to economic change or environmental degradation? Well, it's not true that you can induce a frog to willingly remain in boiling water by starting it off in cold water. But that does not diminish the truth of the message that the accumulation of imperceptible changes can have a significant effect on the economy and the environment. We need to be aware of what changes are occurring and to respond to them in a timely fashion. The metaphor lies in the frog's ability to escape from the container: if there's no way out, then the frog's fate is a foregone conclusion.