How are heat flow and air movement related to the formation of thunderstorms?

The best way to respond to this, in my opinion, is to simply describe how a thunderstorm forms.

The initial requirement is unstable air, which is characterized by an environmental lapse rate steeper than the mean environmental lapse rate (6.0 degrees/km).

After that, a parcel of air must be lifted by one of the five lifting processes (orographic, convection, convergence, frontal, or mechanical). Whichever lifting process takes place, the parcel of air will cool at the dry adiabatic lapse rate (10 degrees/km). Eventually, the temperature of the parcel will reach the dew point, or 100% relative humidity, depending on its humidity. This point is known as the lifted condensation level (lcl), and it is where clouds begin to form.

The parcel of air is now cooling at a slower rate than the environment; as a result, at some point the rising parcel of air will become warmer than the surrounding air and it will then be buoyant and keep rising on its own. This is known as the level of free convection (LFC). If the parcel of air is lifted further, it will now cool at the saturated adiabatic lapse rate (5.0 degrees/km). It is a shallower lapse rate because the process of condensation releases latent heat (heat trapped in water vapor from the process of evaporation) as sensible heat (heat you can feel).

This is the equilibrium level (EL), where the rising parcel of air will eventually lose its buoyancy due to the environment lapse rate becoming negative (becoming warmer as one rises). The air parcel does not stop rising at this point because, from the LFC to the EL, it will have picked up a lot of inertia, and it will continue rising until this inertia is spent. This will be the top of the cloud, and if the cloud is large enough, it will form a cumulonimbus and a thunderstorm.

To put it briefly, heat and air traveling upward from water vapor into the surrounding air.

Heat flow and air movement contribute to thunderstorm formation as warm, moist air rises, cools, and condenses, releasing latent heat. This process fuels updrafts, creating instability and driving the development of thunderstorms.