Cheese should be added to a Mornay sauce off the heat to prevent it from separating, becoming stringy, or developing a grainy texture. High heat causes the proteins in the cheese to break down and the fats to separate, resulting in an undesirable sauce consistency. Gently stirring the cheese into the already-cooked béchamel base, while the sauce is still warm but not simmering, ensures the cheese melts smoothly and creates a creamy, luxurious sauce.