Nah - the pot stays hot for hours and is still very warm in morning in a heated house. The broth is brought to a boil again before simmering again anyway.
Paleo-keto physician Dr. Sarah Myhill maintains a continual bone broth pot on her wood stove, topping it up with water & bones, the old way, very witchy. Wood stoves are allowed to die down to embers at night, then stoked and refueled in the morning. Main thing is to always bring the broth to a boil again before either serving or simmering more