The damage bonus is applied in the same way that the bonus from Fireball Frenzy is. The Smite Infusion page has in-depth details on how elemental damage bonuses apply to different weapons and abilities.
Note that the debuff from Accelerant is still applied. Thus, damage output is increased and enemies become more susceptible to said damage. This can lead to a dramatic increase in damage dealt to affected enemies, even with weapons without innate Heat damage, as long as the Heat does not combine with other elements (e.g. a weapon built for Viral and Heat damage used against Grineer whose armor has been completely removed with Corrosive Projection). This is especially true with high Ability Strength builds.
The bonus Heat damage has the potential to create combined elements on the weapon or increase the damage of combined elements already present. If this happens, the bonus won't be able to take advantage of the debuff since it only affects base Heat damage and not combined elements, even if part of the combined element's damage comes from Heat.