Mute Swans drying and tucking foot

Mute swans often stick one foot in the air as they swim (top shot) easily steering themselves with the other foot. I had often wondered what the purpose of this habit was.
  The two Mute Swans in my local park have afforded close observation in the last couple of months. Last week I noticed that sometimes they have one of their legs tucked under their flank feathers, virtually invisible, only a bit of the 'knee' showing, while swimming with the other leg. This behaviour probably results in keeping one leg quite warm under the plumage.
Yesterday I put both behaviours together by watching how the young swan took one foot out of the water, shook it and left it out for a while. Then it behaved like it wanted its leg dry before tucking it under its feathers: it tucked his leg under the feathers, but seemed not to be happy about it and it stuck it out again and shook it a bit more before finally tucking it in for good.
 I had noticed that cygnets, even before they have feathers, have this habit of tucking a leg out of the water over their body. I just had never realised the adults would do it too, preceded by the leg-stuck-out while drying.
This behaviour has also been reported in other swan species and although thermoregulation seems to be the underlying reason, both cooling and drying/warming have been proposed as explanations for the behaviour.
 The next series of photos illustrates the sequence of behaviour.

The following photo is from 21 June of 2015, taken in a local fishing lake. A young downy cygnet a few weeks old. You can notice how its right leg is tucked by its body, outside of the water, while it preens. When it grows feathers, the same position results in a leg completely covered with feathers.

More information

Why do some swans only paddle with one leg, with the other leg tucked up under the wing?

The Whooper Swan. Here. p 93-94.