Earlier quoted context omitted.
Has that kind of metaphor ever helped in a real case/conversation you know of? The metaphor illustrates how what you're saying might be true and helps understand what you mean. Somebody who disagrees usually understands what you mean by "it's getting warmer". They just don't believe it. At least that's my experience. Convincing someone in such matters is completely impossible unless there is a prior personal relation…
Trying to convince someone opposite of something they really really believe in has a very low probability of success, you will just ground them more into their belief. There are different pathways, but they take empathy and patience, some traits a lot of people lack when communicating with counter parties.
At the extreme end deprogramming the is often referred to in terms of ‘cult deprogramming’ but it’s more widely applicable and more effective than it has any right to be. Clearly unacceptable in this context, but worth understanding from a psychological perspective.