Heat is energy — and when energy enters a gas, the molecules that make up that gas start moving faster. Faster-moving molecules spread further apart, taking up more space. Think of a school corridor at the end of the day: when students are tired and shuffling slowly, they pack in tightly together. 

Give them Friday afternoon energy and they spread out — the same number of people suddenly needs far more space. Hot air molecules are those Friday afternoon students. They spread out, take up more volume, and so the same mass of hot air occupies more space than the same mass of cool air. That makes hot air less dense — lighter per cubic metre — than the cool air around it.

Less dense things rise above denser things. That is buoyancy, and it works in air just as it works in water. A bubble of hot air rises through cool air the same way an air bubble rises through water. As the tea bag burns, it heats the air trapped inside the paper cylinder. 

That hot air rises upward through the cylinder in a continuous column — a thermal. You cannot see it, but it is there from the moment the flame is lit. The rising thermal is also what makes the flame itself lean and flicker as cool air rushes in from the sides to replace the hot air that has risen away.

The launch happens at the last moment because weight is the key variable. While the paper bag still has any structure left, it is too heavy for the thermal to lift. But as the final fibres burn away, the cylinder becomes a hollow shell of ash — almost no mass at all. At that moment, the upward force of the thermal finally overcomes gravity, and the Phoenix rises.

The same physics drives every hot air balloon ever built, every thunderstorm ever formed, and the convection currents that carry heat through the Earth's mantle and move tectonic plates. Your tea bag just demonstrated the engine that powers the planet's weather.

To see convection in slow motion — a snake that spins silently above a warm lamp as rising air pushes through its coils — try [The Sleeping Snake]. And for another experiment where invisible air pressure does something unexpected, [The Gravity Battlefield] shows hot air's cousin — fast-moving air — holding a balloon up against gravity using Bernoulli's Principle.