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
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.