Rollock explains that temporary faith is different from historical faith (and other sorts of non-soteric faith) and that it shares many elements with justifying faith. Rollock says:
The reason of the name is this; it is called Temporary, because it endures but for a time, because it hath no root.
It hath the same object with justifying faith, and which is properly so called, namely Jesus Christ with his benefits, offered in the word of the Gospel and in the Sacraments; wherein it differs from historical faith, which hath for the object thereof the universal truth. It hath the same subject with justifying faith; for it hath its meat both in the mind, and also in the will and heart.
Commenting on James 2:21, Diodati writes:
We must of necessity distinguish the meaning of this word justifie, which is used by St. Paul, for absolving a man as he is in his natural state, bound to the law, and subject to damnation for his sin, which God doth by a rigid act of justice, that requireth full satisfaction, which seeing he could not get of man Rom. 8.2, he hath received at Christ’s hand (who was the Surety) imputed to man by God’s grace, and apprehended by a lively faith. Whereas St. James takes the same word for the approving of man, in a benigne and fatherly judgment, as he is considered in the quality of God’s child, and living in the covenant of grace, as having the two essentiall parts of that covenant joyned together, faith to receive God’s grace and Christ’s benefit, and works to yield him the duties of service and acknowledgement; and this justification is no longer opposite to the condemnation of a sinner in generall, but to the particular one of an hypocrite, who rending asunder these two inseparable parts, sheweth that he hat neither the one nor the other: see Luke 17.19.
~ Pious and learned annotations upon the Holy Bible 3rd ed. (London : Printed by James Flesher for Nicholas Fussell, 1651).