The willow tit is quite stiff in the morning, but 10-15 minutes later temperature is back to normal. If a hungry weasel suddenly starts nibbling her rear feathers, she wakes up a lot faster.
The bird weighs 11 grams in the morning. She eats a little extra in the day to survive the nocturnal energy requirements: one gram of fat is addad to the body weight. This is consumed at night-time, and is exactly what is needed to keep up its body temperature.
Why only add one gram of fat? Why not more as precaution? They also have to deal with predators – weasels, hawks and pygmy owls. A limber bird escapes faster! It's a delicate balancing act!