Ballooning depends on the basic premise that warm air rises. It rises because it is less dense than the surrounding ambient air. If this warm air is contained in an almost enclosed container, it will exert upward pressure on that container until that force equals the weight of the container. In the case of a balloon the container is the fabric “envelope”.
When the upward force equals the combined weight of all the components of the balloon system (basket, fuel, burners and envelope), plus the weight of the passengers, the balloon is said to be in a state of “equilibrium”. It neither climbs nor descends. It has neutral buoyancy. That temperature is called “equilibrium temperature”
If we heat the balloon, say 10 degrees warmer, it will begin to climb at a certain rate. If we heat it even hotter it will climb at an even greater rate.
Conversely, if we are flying at altitude and allow the envelope to cool to below the “equilibrium” temperature, it will begin to descend at a proportional rate.
In theory if we applied just enough constant heat to the balloon to compensate for natural heat loss through the fabric we could fly at a constant altitude, by maintaining this equilibrium temperature.
The current hot air balloon burners make quite a bit of noise so we elect to put up with a very loud noise for a few seconds (slightly overheating the envelope) and allow it to start a climb. We can then “coast” in absolute quiet for a minute or so before once again applying full heat. Thus the horizontal flight path of the balloon actually becomes a sine wave.
Keep in mind also that the balloon system does have mass even though it may be “lighter than air”. The envelope alone of an average balloon can contain a couple of tons of trapped air. This mass has inertia and momentum. Thus when you want to initiate or stop a climb or descent you must overcome these forces. So, response time is not instantaneous. It’s kind of like driving an old heavy Cadillac using a Volkswagen engine and brakes. You have to plan ahead!!