DOES GOD HEAR THE PRAYERS OF THOSE WHO ARE IN MORTAL SIN?

In a sinner we have to consider two things: his nature, which God loves; and his fault, which God hates. If, then, a sinner asks something of God formally as a sinner --that is, according to his sinful desires-- God, out of His mercy, does not hear him, though sometimes He does hear him in His vengeance, as when He permits a sinner to fall still farther into sin. 

But that prayer of a sinner which proceeds from the good desire of his nature God hears, not, indeed, as bound in justice to do so, for that the sinner cannot merit, but out of His pure mercy, and on condition, too, that the four above-mentioned conditions are observed -- namely, that he prays for himself, for things needful for his salvation, that he prays devoutly and perseveringly.

Summa Theologica, II-II, 83, 16, by Saint Thomas Aquinas.