And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; even the Spirit of truth...for he dwelleth with you, and shall be in you. John 14:16, 17.
A new heart is not necessarily a cleansed heart. A new mind in not necessarily a cleansed mind. This is why the continuing work of the Holy Spirit is a necessity. The Holy Spirit can convict us of sin and lead us to conversion, to being born again, but that is only the beginning. His work does not stop there. In Steps to Christ, page 18 we are told that when we receive a new heart, this leads to a new life. Conversion is only the beginning--it is not the whole picture.
The regenerating work of the Holy Spirit simply prepares us for His further work, which is the cleansing of the Christian. What does it mean to be cleansed by the Holy Spirit? Jesus said that He would pray the Father and we would be sent another Comforter to abide with us. It would be the Spirit of truth, who would dwell with us and would be in us. The New Testament teaching is that there is an indwelling presence of God, which gives transforming, overcoming power. We are told that a new heart will be given to us. If we confess our sins, God will forgive and cleanse us from all unrighteousness (1 John 1:9). What does this mean? Is it simply cleansing the records of heaven? No, it is cleansing us. And it is through the Holy Spirit that this happens.
Notice Ephesians 3:16-19: "He would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man; that Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love, may be able to comprehend with all saints what is the breadth, and length, and depth, and height; and to know the love of Christ."
"Sin could be resisted and overcome only through the mighty agency of the Third Person of the Godhead....It is the Spirit that makes effectual what has been wrought out by the world's Redeemer. It is by the Spirit that the heart is made pure. Through the Spirit the believer becomes a partaker of the divine nature. Christ has given His Spirit as a divine power to overcome all hereditary and cultivated tendencies to evil."--The Desire of Ages, p. 671. It is through the Holy Spirit's cleansing that we can overcome.