Depends what timeframe you're talking about. As stars burn they get hotter, and eventually bigger. So yes, climate change will eventually end humanity though this would be the later scale.

>smaller global population surviving

This is just an unfound assumption on your part. Passenger pigeons went from billions of birds to extinct in less than a century. There are hundreds of different scenarios around climate change and disease evolution alone that could wipe us pretty quickly and a rapidly falling population would make it worse quickly as things like new medicines could not be developed quickly enough, or more technology couldn't be created fast enough (unless we have full AGI working on itself, but then you have alignment being its own problem).