Why do we shiver?
Cold outside? Your muscles wiggle to make heat, and tiny ones pull your hairs up.
Muscles wiggle to make heat
When you get cold, your brain tells your muscles to tighten and loosen very fast, about ten times a second. You cannot stop it. All that wiggling makes heat, the same way running warms you up. That is shivering. Your teeth chatter because the jaw muscles join in.
Shivering is heat made by muscle: the hypothalamus drives rapid, involuntary, rhythmic contractions of skeletal muscle at roughly 8 to 12 cycles a second. Because the muscles do no useful work, almost all the energy they burn becomes heat, and heat production can rise to several times the resting rate. Shivering starts in the trunk and jaw and spreads to the limbs. Newborn babies shiver poorly and instead burn brown fat, a tissue built to make heat. The jiggle here is scaled up so you can see it.
Goosebumps
Feel the little bumps on your arm when you are cold? Every hair has a tiny muscle at its root, far too small to show here. When those muscles pull, the hair stands up and the skin around it bunches into a bump. On a furry animal, fluffed-up fur traps warm air. We lost most of our fur, so we just get the bumps.
Goosebumps (piloerection) come from the arrector pili, a strand of smooth muscle attached to each hair follicle. Cold, fear or strong emotion fire the sympathetic nerves, the strand contracts, the hair tilts upright and the skin over the follicle dimples. In furred mammals this thickens the layer of trapped air for insulation and makes the animal look bigger when threatened. In humans it is a leftover reflex with little effect on warmth. Neither skin nor these tiny muscles are in this model, so the bare arm stands in.
Your thermostat
Deep in the middle of your brain is a tiny part called the hypothalamus. It works like a thermostat and keeps you at about 37 degrees. Too cold? It starts the shivering and narrows the blood pipes in your skin so heat stays inside. Too hot? It makes you sweat and sends blood to your skin to cool off.
The preoptic area of the hypothalamus collects temperature signals from the skin and from the body core and holds the set point near 37 °C. Cold responses, roughly in order: narrowing of skin blood vessels, goosebumps, behaviour (curling up, seeking warmth), shivering, and heat from brown fat. Warm responses: widening of skin vessels and sweating. A fever is the set point deliberately raised by the immune system, which is why you shiver and feel cold at the start of one even in a warm room.