Domestic cats don’t always curl up when they sleep but they often do. It’s the default position. Although, we do see some extraordinary sleeping styles for the domestic cat; being totally stretched out is also not uncommon inside the home. But being curled up and stretched out are linked. I’ll explain what I mean. And there are 2 reasons for being curled up.
Warmth
Domestic cats curl up when they sleep because it keeps them warmer than when stretched out. They present less surface area of their body to the air around them. This means that less body heat is lost. This in turn keeps them warmer. It’s about surface area and heat loss through the skin notwithstanding the fact that the fur helps to keep heat loss to a minimum.
And of course, when a body is curled in on itself those parts that would be exposed to the air are now in contact with other parts of the body and so they heat up those parts. Once again, it’s a question of not losing body temperature to the air but to use it to warm other parts of the body.
If a cat is stretched out when sleeping is because the ambient air temperature is warm. This will happen most often when they are sleeping inside a warm home. Or they are on your lap and soaking up the heat from your body. There is no need to retain body heat under these circumstances. Sometimes they may even want to lose it because it’s too warm.
Security
As the original cat coat is a striped tabby, when a domestic cat is curled up they look like a snake which is a defensive position helping to keep them secure from predators. We are going back to the origins of the domestic cat and their wild Ancestor the North African wildcats. The picture illustrates this effect.
Tiger size and climate
The same physics applies to the reason why Siberian tigers are larger than Sumatran tigers. Siberian tigers live in cold weather whereas the opposite is true for Sumatran tigers. Siberian tigers are the world’s largest cat and the largest tigers whereas Sumatran tigers are the smallest tigers. In terms of surface area in relation to body mass, the Siberian tiger has a smaller surface area compared to the Sumatran subspecies. It’s about heat loss and surface area once again.
In this instance evolution dealt with a survival issue by making Siberian tigers bigger than Sumatran tigers. Evolution decided that tigers in cold and often freezing climates needed to be larger than standard to survive. Over the couple of million years of tiger evolution they became bigger. The same by the way applies to the mountain lion a.k.a. puma. The pumas in Canada are bigger than those in South America because of the extreme temperature difference between those two parts of the world.
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