The boiling frog is a parable describing a frog being slowly boiled alive. The premise is that if a frog is put suddenly into boiling water, it will jump out, but if the frog is put in tepid water which is then brought to a boil slowly, it will not perceive the danger and will be cooked to death. The story is often used as a metaphor for the inability or unwillingness of people to react to or be aware of threats that arise gradually.
While some 19th-century experiments suggested that the underlying premise is true if the heating is sufficiently gradual, according to contemporary biologists the premise is false: a frog that is gradually heated will jump out. Indeed, thermoregulation by changing location is a fundamentally necessary survival strategy for frogs and other ectotherms.