From World Bird Sanctuary
Many times we will get asked by visitors, "Does this bird only have one leg?" Don't worry, they all have two! Birds, such as Farnsworth the barn owl, will stand on one leg for a few reasons.
One such reason is to help with heat loss. The arteries that transport blood into the legs lie in contact with the veins that return blood to the bird's heart. The warm arteries heat the cooler veins. Since the veins also cool the arteries, the bird's feet are closer to environmental temperature and thus don't lose as much heat as they would if they were at body temperature. Even so, on extra cold days, tucking a foot up and keeping it close to their warm body will reduce heat loss even more.
But what about the birds that you see tucking a leg on a hot day in the middle of summer? The other reason why birds will stand on one leg is simply that it is comfortable. When a bird is relaxing, they will regularly stand on one leg instead of both.
Now we know the reason!