I suppose it is (sometimes) exactly the same for birds as for planes.
[same]
Newton's second law tells us that Force = mass times acceleration, and Newton's 3rd law tells us that for every force there is an equal and opposite reaction. Because both airline and bird wings are fixed size, they interact with a fixed volume of air, meaning if the air is less dense, they will get less force against their wings as they push the air down. Thus they generate less lift.
[not same]
However, unlike planes, birds don't use jet engines to suck in air (which will be less dense) to generate their forward velocity at takeoff. Instead they usually run on the ground or jump. Their ability to run on the ground or jump should not be affected by air density. I believe for most birds, taking off is the limiting factor, not sustaining flight once airborne. Thus, birds should be able to continue flying.
But, once airborne, will hotter temperatures affect their migration? Probably not too much as the CNN article you link to says for planes the effect is 1% for 3 degrees celcius, meaning if the earth warms 3 degrees, birds will only have to expend 1% more energy. Now it could get worse in some areas, but birds can also move, and if a wind pattern changes, they can just fly to a different area where the wind pattern still exists, so hopefully they'll be alright.
But I don't know enough about bird behavior to say for certain. But from a physics perspective, there's no reason to suspect birds have it worse than planes in terms of what their wings can do with the air, so if planes lose 1% energy for every 3 degrees warming, birds should lose even less than 1% energy. Hopefully the planet won't warm much more than 3 degrees. :)
As a final note, once the bird is flying high in the sky, the air temperature should no longer be scorching like it is at ground level, so even though the ground might be 20 degrees hotter, the higher up air probably won't be that much hotter, and remember that near the ground at takeoff, birds get their power from their legs, not wings.