A fellow in the dialect blog thinks there is no relationship. It’s theoretical, though. No data.
Climate change will affect the environment in ways that have a significant impact on living conditions. As a result, indigenous and poor people are much more likely to be forced to relocate and to undergo severe changes in their communities. These changes may well lead to the dissolution of the community and the loss of schools that teach in their language. So yes, one could argue that languages could be lost as a result of climate change or as a result of natural disasters.
This is an indirect affect, and it seems reasonable to me. But direct affects seem unlikely based on the little research I’ve done. I will note that there is very little out there about this topic—at least that I could find in the short amount of time I can put into these answers.