The latter mistake has nothing to do with language. In general, things that feel cold have lower temperatures, and things that feel hot have higher ones; unless you carry a thermometer around everywhere, it's easy to assume that the correlation is perfect, and anything that feels colder has a lower temperature. But in the former, prescriptivist fallacy, language plays a crucial role. This fallacy consists of redefining a well-known popular term for scientific purposes and then declaring its original meaning wrong, forgetting that its original meaning was based on quite different principles. A similar example which I came across recently is the notion that the Bible was mistaken in listing the bat as a bird, or rather the ʕǎṭallēp as a ʕôp (via); it should be obvious that if everyone was calling bats birds, then "bird" (or rather ʕôp) did not mean "member of the clade Avialae" at the time! In this case, however, the new meaning has gained enough popular acceptance in English to have driven out the old one almost entirely, thereby making Bible translators' lives harder but biology teachers' lives easier. (I covered a similar Qur'ānic misunderstanding involving "atom" a while back.)
Usually, prescriptivism involves declaring that a new (or allegedly new) meaning or usage is wrong. Scientists' prescriptivism is rather the inverse, in that it consists of declaring an old, previously generally accepted meaning or usage wrong. At its best, this can be an effort to popularise knowledge: everyone ought to know that bats are more closely related to humans than to sparrows, and if we can just persuade them to stop calling bats birds, they'll remember. But, fundamentally, this is also a power grab: we're the experts on this field, so we're the ones who get to say what the word means, not you. Giving old terms new definitions can be useful, but we should never forget that that's what we're doing.
Have you come across any examples of the scientists' prescriptivist fallacy lately?