If I believed in BoD, I would have to concur with Innocent III that it remits temporal punishment due to sin also.
There can be no entry into the Kingdom of Heaven without being born again. Rebirth clearly means regeneration (where the entire creature is renewed), and Trent taught that initial justification is a regeneration and then that regeneration entails complete remission of all sin and of all punishment due to sin.
This made-up theory that BoD doesn't remit temporal punishment due to sin is highly problematic.
This here is an extremely solid argument that I can find no fault with, except that it doesn't refute BoD per se, but does clearly refute the notion of BoD that holds temporal punishment is not remitted by it:
[VATICAN CATHOLIC DOT COM]/man-must-regenerated-refutes-baptism-desire/