According to the 2010 State of the Birds:

Oceanic birds are among the most vulnerable species because they don’t raise many young each year; they face challenges from a rapidly changing marine ecosystem; and they nest on islands that may be flooded as sea levels rise. All 67 oceanic bird species, such as petrels and albatrosses, are among the most vulnerable birds on Earth to climate change.

Puffins are at risk because they are particularly vulnerable to the effects of climate change. Read more on their website.