Mammals are more adept to adapting to climate change. Reptiles on the other hand have a very hard time dealing with even a few degrees of temperature change from there norm.
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...
But plenty of reptiles survived just fine. It's as if there were something special about dinosaurs. Could there have been some major virus that wiped them out and left other species untouched?
His question was to why "small dinosaurs" did not have the same chances as mammals.
Large dinosaurs(there were no large mammals, but if there were it would apply the same to them) had different issues then the rest, mainly two different things, food and oxygen.
The first reason food, is the main reason. These large animals required huge amounts of food to survive. As the ecosystems collapsed the available food supplies dropped to almost nothing.
The second reason and the same that animals grew to be so large during this time period is predominantly because the oxygen levels were much much higher then they are now. As the ecosystem collapsed so did the oxygen levels. This is why we do not have larger animals now.