Heat travels through the air through a process called convection. To understand this, it is important to understand a few things about energy. An object can have potential energy or kinetic energy. Potential energy is the energy an object has due to its position. If you hold a ball waist-high in your hand it has some potential energy. If you raise the ball above your head, the potential energy has increased because its position has been increased relative to its normal position on the ground.
Kinetic energy is the energy of motion. The more kinetic energy they have, the lighter they are. The less kinetic energy, the heavier or more dense they are. Cold air does not have a great deal of kinetic energy, therefore it moves more slowly. Another way to think about this is to say that the more energy, or more specifically absolute temperature, air molecules the more they expand, if some other conditions are constant. This direct relationship is seen in Charles Law, named after a nineteenth century French scientist who studied gas laws, as mentioned by David N. Blauch.
Since warm air has more kinetic energy, due to its increased temperature (hence the description "warm") it expands and therefore "rises" compared to cold air. This is why in homes, the top floor can get warmer more naturally than the lower floor.
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