Why does a hot air balloon comes down long after burner is switched off?

A hot air balloon descends slowly after the burner is switched off because the air inside the envelope gradually cools, causing the balloon's lift to decrease. The rate of descent is influenced by the thermal inertia of the air inside the balloon and the ambient temperature outside. Additionally, the balloon's buoyancy is still sufficient to keep it afloat for some time, allowing it to descend gently rather than plummet. The descent can also be moderated by the design of the balloon and the weight of the payload.