I've realised that I've read a number of books where climate change is one of the key themes of the book (although that's not the reason I read them).
They're certainly not going to add anything a visitor to this site doesn't already know, but might make a good gift for a family member who might otherwise lack engagement on the subject.
I'm a fan of dystopian sci-fi (although I prefer it to stay fictional), and the first books are in that genre:
First up is Margaret Atwood with Oryx and Crake and Year of the Flood. Set in a high-tech, high polluting near future, sea levels have risen at catastrophic rates due to methane bubbling up out of the permafrost, the weather is hot, hot, hot and humid with big storms (it's not spelt out, but the novels appear to be set in Boston) and rich people take summer holidays on the shores of Hudson Bay. Polar bears are gone - one of the characters worked for Operation Bearlift in his past.
Second is Paolo Bacigalupi with The Wind-up Girl (and adult novel) and Ship Breaker (a teen novel). These are set in a high gene tech, high poverty, low energy future. The wind-up Girl only has oblique mentions to climate change, such as high sea levels and restrictions on the use of coal, but Ship Breaker paints a strongly dystopian climate change future. The main protagonist (a teenage ship breaker) lives on the shore of the Gulf of Mexico, sea levels have risen, cities have drowned and Cat 5 hurricanes are a regular occurrence in the Gulf. The description of a partially drowned but still functioning New, New Orleans is excellent. The main character dreams of working on a clipper ship, and has a picture on the wall of his hovel, of a clipper sailing across the arctic ocean, with ice crystals forming on the rigging. It is still a teen novel, and the final chase and fight scene which occupies the last quarter of the book doesn't have much for the adult reader.
In the category of General Fiction we have:
Barbara Kingsolver with Flight Behaviour. I do like Kingsolver, although her novels can feel a little bit educational sometimes, although this novel entertains well enough, you don't really notice. It's set in rural Tennesse, and the plot revolves around Monarch butterflies that have unexpectedly overwintered in the mountains there, due, of course, to climate change. The novel paints a sympathetic and often entertaining picture of the locals. It's not a climate change doom novel, dealing with the more subtle and near-term effects and so is unlikely to put people off with 'alarmism'.
Lastly, Ian McEwan with Solar. This is a highly entertaining satirical book, with a thoroughly repulsive central character. The author even pokes fun at some of the plot ideas in some of his earlier books. A lot of information is imparted to the reader, but it doesn't feel at all heavy. The only problem I see is that some readers may also think that the climate change message is also intended as an object of fun. Not everyone gets satire.
