There is proof of it. Such as fossils, records, videos, etc. Dinosaurs and Thylacines for example. Both of these have been extinct for quite some time. Although there is footage of some Thylacines there isn't any of any Dinosaurs. However, there is fossils and bones found from Dinosaurs. There has been fossils from many extinct animals dating back millions of years, therefore proving its a common event through history.
When the homeostasis senses that your too cold, it sends signals to your muscles that make your shiver and create warmth. This is called maintaining the homeostasis.