Ecplanation: Hot air balloons float due to the buoyant forces that act on them.
When air is heated, the air molecules spread farther apart. This causes the density of the hot air to be less than the density of the cold air.
Eventually, buoyancy causes the balloon to rise because the weight of the cold, outside air that is displaced by the balloon is greater than the weight of the hot air inside the balloon (plus the weight of passengers and balloon equipment).