St. Augustine was referring to the mind that has been "conformed to God" as described in Reading "Mere Christianity" and having a hard time with book III, chapter 12.
This is based on established doctrine, common to most denominational views, of Sanctification.
Progressive sanctification
"Indeed, the more sanctified the person is, the more conformed he is
to the image of his Savior, the more he must recoil against every lack
of conformity to the holiness of God. The deeper his apprehension of
the majesty of God, the greater the intensity of his love to God, the
more persistent his yearning for the attainment of the prize of the
high calling of God in Christ Jesus, the more conscious will he be of
the gravity of the sin that remains and the more poignant will be his
detestation of it....Was this not the effect in all the people of God
as they came into closer proximity to the revelation of God’s
holiness.
The doctrine of Sanctification has Scriptural support in Romans 6:22, 1 Corinthians 6:11, 2 Corinthians 3:18, 2 Corinthians 7:1, 1 Thessalonians 4:3, 1 Thessalonians 5:23, Hebrews 6:1, Hebrews 12:14, James 1:4, and others.
Th most clear Biblical passage, however, which directly answers your question is Romans 12 (the following from the NASV) It starts by telling us to be conformed to God, and then expands on what a conformed mind produces for fruit, showing that a conformed mind does good, naturally.
1Therefore I urge you, brethren, by the mercies of God, to present
your bodies a living and holy sacrifice, acceptable to God, which is
your spiritual service of worship.2And do not be conformed to this
world, but be transformed by the renewing of your mind, so that you
may prove what the will of God is, that which is good and acceptable
and perfect.
3For through the grace given to me I say to everyone among you not to think more highly of himself than he ought to think; but to think
so as to have sound judgment, as God has allotted to each a measure of
faith.4For just as we have many members in one body and all the
members do not have the same function,5so we, who are many, are one
body in Christ, and individually members one of another.6Since we have
gifts that differ according to the grace given to us, each of us is to
exercise them accordingly: if prophecy, according to the proportion of
his faith;7if service, in his serving; or he who teaches, in his
teaching;8or he who exhorts, in his exhortation; he who gives, with
liberality; he who leads, with diligence; he who shows mercy, with
cheerfulness.
9Let love be without hypocrisy. Abhor what is evil; cling to what is good.10Be devoted to one another in brotherly love; give preference
to one another in honor;11not lagging behind in diligence, fervent in
spirit, serving the Lord;12rejoicing in hope, persevering in
tribulation, devoted to prayer,13contributing to the needs of the
saints, practicing hospitality.
14Bless those who persecute you; bless and do not curse.15Rejoice with those who rejoice, and weep with those who weep.16Be of the same
mind toward one another; do not be haughty in mind, but associate with
the lowly. Do not be wise in your own estimation.17Never pay back evil
for evil to anyone. Respect what is right in the sight of all men.18If
possible, so far as it depends on you, be at peace with all
men.19Never take your own revenge, beloved, but leave room for the
wrath of God, for it is written, “VENGEANCE IS MINE, I WILL REPAY,”
says the Lord.20“BUT IF YOUR ENEMY IS HUNGRY, FEED HIM, AND IF HE IS
THIRSTY, GIVE HIM A DRINK; FOR IN SO DOING YOU WILL HEAP BURNING COALS
ON HIS HEAD.”21Do not be overcome by evil, but overcome evil with
good.
It cannot be applied to the natural, sinful mind; only to the mind that has been conformed and the Christian that is in agreement with God.
Romans 8:7-11
7because the mind set on the flesh is hostile toward God; for it does
not subject itself to the law of God, for it is not even able to do
so,8and those who are in the flesh cannot please God.
9However, you are not in the flesh but in the Spirit, if indeed the
Spirit of God dwells in you. But if anyone does not have the Spirit of
Christ, he does not belong to Him.10If Christ is in you, though the
body is dead because of sin, yet the spirit is alive because of
righteousness.11But if the Spirit of Him who raised Jesus from the
dead dwells in you, He who raised Christ Jesus from the dead will also
give life to your mortal bodies through His Spirit who dwells in you.