The newly warmed air also rises. As the warm air gets close to the ceiling, it loses some heat. Now this air is cooler. It follows the cool air which is falling. The cool air falls and then is drawn upwards again.
Convection causes currents of warm and cool air to move.
Notice how convection is happening in this pan. The process is the same in water and in air. It even happens in the hot magma inside the earth. Hot air, hot water, and hot rock all tend to rise. Cold creeps lower.