Separation of fat from hot milk

Well, you can if you like. It actually isn't really stable at room temperature either. As the temperature rises, it increases the pressure within the bubble held by the fat layer- until the point that the fat can't contain it any longer. The emulsion breaks as that happens. Stirring would hasten the process, regardless of the temperature, because the action of stirring would also fracture the bubble walls and release the trapped air. There isn't any protein in whipped cream either. It's all fat, water, and air. In order to prevent the separation of fat from the milk solids, you would have to homogenize the whole mixture. That would require you to force the cream through a very tiny nozzle under pressure, to reduce the size of the fat molecules and allow them to be equally distributed in the milk. Stirring will do the task temporarily, but it is quite natural for the milk fat to rise to the top of the milk. Fat molecules are denser than the milk proteins suspended in water you recognize as liquid milk. Unless the mixture is homogenized, they will always float to the top over time, even if chilled. The whipped cream will break down over time as well, because gravity works and the pressure within the little air pockets will manage to break through. There are a few ways to delay the process, like with the use of gelatin, which allows the whipped cream to retain shape at room temperature and slightly higher for a few hours.