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.