The words "our heavenly residence" means the same thing as "the place God will give us to live in." Paul speaks of the new body that believers receive after they die as if it were both a house to live in and a piece of clothing that a person can put on. Paul knows that when he dies he will receive a much better body. Because of this, he is not afraid of being killed for preaching the gospel. So he tells others that they too can be reconciled to God. Christ will take away their sin and give them his righteousness.