Birds are not strictly "warm blooded" as mammals are, but yes they are not strictly cold blooded ether. They are able to generate their own body heat to some extent yes, but are still fare more susceptible to climate change then a mammal would be.
I don't know about birds during these "dark" times, but todays birds are pretty resilient to wide change in temperature even on a daily basis. They are capable of generating and circulating fair amount of body heat. Their average temperature is typically much higher than mammals. They are also well insulated, more than humans, apes, dogs, cats...
