Question

Why does the hot air balloon stop rising when all the air inside it turns hot??

Answer 1

The balloon will stop rising if the upward buoyant force is overcomed by the downward gravitational force. This will happen if the balloon reaches a height where density of air is nearly equal to the density of hot air within the balloon. Or if the air within the balloon cools down. In these cases the upward thrust will be reduced and the balloon will start moving downward.