When "Gift of Furious Might" boosts Damage that's limited in some way – like the first level of Rising Heat's innate, which only damages Explorers – is the bonus damage also limited?

When "Gift of Furious Might" boosts Damage that's limited in some way – like the first level of Rising Heat's innate, which only damages Explorers – is the bonus damage also limited?

Yes.
This is true for all sorts of limitations - type of piece that can be damaged, number of pieces that can be damaged ("Veil the Night's Hunt" / "Tempest of Leaves and Branches"), etc.