Observe what happens top the balloon as it rises. Does the balloon fly better when the room is cooler or warmer. Measure the velocity of the balloon by timing how long it takes to reach the ceiling. This is why cooking oil floats on top of the water. A simple experiment with an ice cube in a cup of water proves that ice is less dense than liquid water.
Hot air is less dense than cool air and thus rises.
This lifting force is the result of Archimedes' Principle in action. Archimedes's Principle states that object placed in a liquid seems to loose an amount of weight equal to the weight of the fluid it displaces.