Hot Air Balloons
If you fill a bottle partway with very hot water, then stretch a balloon over the top, the balloon will inflate slightly over the next few minutes. The same thing happens if you stretch a balloon over an empty bottle, then stick that bottle in a bowl of hot water. It is not the water, but the heat in the water that is causing the balloon to inflate. You may not know it, but you are actually creating your own hot air balloon.
What is Heat?
When the air in the bottle is placed close to hot water (either by adding the water to the bottle, or by submerging it in a bowl), the air absorbs some of the heat from the water. Heat is a measurement of the motion of molecules. The hotter the temperature, the more quickly the molecules move around inside the air.
Heating a Gas
Solids stay about the same size as long as they are solids, and liquids do the same thing as long as they are liquids. Gasses, however, don't. The molecules in a gas are not bound together. When they are heated, they spread out, flying in all directions at a higher rate. If they are kept in a container, such as a bottle with a balloon on top, they strike the sides of the container more forcefully.
Pressure and Expansion
The molecules in the air are always creating pressure. Countless molecules collide into everything every second, creating a constant force. Before the air in the balloon is heated, the molecules inside are creating as much pressure as the molecules outside, meaning that the balloon stays at equilibrium and neither expands nor contracts. When they get heated, however, the inside molecules start moving with more force. They create more pressure, causing the balloon to expand outward until the pressure equalizes.