The air is made up of molecules. These molecules bounce off each other all of the time. When an object is warmed, it's atoms move very rapidly. When you heat water, the heat from the water is transferred to the air inside. Molecules move faster and faster and are being bumped and bounced harder.
Molecules move farther apart so the air expands.
As the space between the molecules gets larger, the air takes up more space. This is why the heated balloon will expand during my experiments. How warm or cool something is. The students may need to know how a thermometer works. They also need to understand how the molecules move to make the water cool.