Objection 1. It would seem that faith does not purify the heart. For purity of the heart pertains chiefly to the affections, whereas faith is in the intellect. Therefore faith has not the effect of purifying the heart.
Objection 2. Further, that which purifies the heart is incompatible with impurity. But faith is compatible with the impurity of sin, as may be seen in those who have lifeless faith. Therefore faith does not purify the heart.
Objection 3. Further, if faith were to purify the human heart in any way, it would chiefly purify the intellect of man. Now it does not purify the intellect from obscurity, since it is a veiled knowledge. Therefore faith nowise purifies the heart.
On the contrary, Peter said (Acts 15:9): "Purifying their hearts by faith."
I answer that, A thing is impure through being mixed with baser things: for silver is not called impure, when mixed with gold, which betters it, but when mixed with lead or tin. Now it is evident that the rational creature is more excellent than all transient and corporeal creatures; so that it becomes impure through subjecting itself to transient things by loving them. From this impurity the rational creature is purified by means of a contrary movement, namely, by tending to that which is above it, viz. God. The first beginning of this movement is faith: since "he that cometh to God must believe that He is," according to Hebrews 11:6. Hence the first beginning of the heart's purifying is faith; and if this be perfected through being quickened by charity, the heart will be perfectly purified thereby.
Reply to Objection 1. Things that are in the intellect are the principles of those which are in the appetite, in so far as the apprehended good moves the appetite.
Reply to Objection 2. Even lifeless faith excludes a certain impurity which is contrary to it, viz. that of error, and which consists in the human intellect, adhering inordinately to things below itself, through wishing to measure Divine things by the rule of sensible objects. But when it is quickened by charity, then it is incompatible with any kind of impurity, because "charity covereth all sins" (Proverbs 10:12).
Reply to Objection 3. The obscurity of faith does not pertain to the impurity of sin, but rather to the natural defect of the human intellect, according to the present state of life.
Source: Summa Theologica (New Advent)