I think you'd need to start by getting them to admit that the heat is a problem without mentioning climate change. Don't use any of the buzz words they've been taught how to respond to. Just try to get them to have a conversation where they have to come up with their own answers.

In fact, maybe don't even start off with anything related to the topics they've been told what to think about. Ask about something they care about more directly that isn't on their party's agenda. You'd need to keep at it long enough for them to start understanding you're not their enemy, which could be anywhere from a few hours to a few weeks/months, depending on how deeply entrenched they are. Then, start trying to work towards the lesser issues their authority doesn't bring up often but has expressed an opinion on. Basically, you need to de-indoctrinate them.

If you can get them to talk about an issue without recognizing immediately that they're in danger of contradicting their chosen authorities, then slowly transition towards getting them to talk about more and more "dangerous" topics, you might help them to bridge that disconnect and start thinking critically about the key issues.

That all said, You'll have an easier time working with people who haven't been deeply entrenched in an authoritarian ideology. The less developed their beliefs, the easier it'll be to guide them towards thinking about their beliefs critically. That's one reason it's so important to teach critical thinking in primary/secondary schools.

Nope. Many have had the urge to ask questions literally beaten out of them in their youth.