Through what mechanism does cholesterol act as a stabilizing agent and why does it depend on temperature?

As I understand it, at higher temperatures cholesterol has a tendency to make the membrane less fluid, and at lower temperatures it makes it more solid. My question is, what mechanisms causes this? At lower temperatures does cholesterol interfere with the electrostatic interactions between the tails, thus decreasing their ability to congregate and form more solid structures and at higher temperatures does it provide more places for those interactions to occur, thus decreasing fluidity? If so, why is that temperature dependent? In short, through what mechanism does cholesterol act as a stabilizing agent and why does it depend on temperature?