In a week from today, I will be giving the Psalm explanation at church over Psalm 15. I have been reading through Calvin's commentary on the Psalm. In verses 1 and 2, David says "LORD, who may dwell in your sanctuary? Who may live on your holy hill? He whose walk is blameless and who does what is righteous, who speaks the truth from his heart" Calvin makes an interesting point on the last phrase of this verse "who speaks the truth from his heart."
David doesn't say "who speaks the truth in his heart" rather David expresses the harmony between our speech and heart, that the two are intricately connected. As tree branches stem from the roots so do our speech stem from our hearts. Furthermore, the one who may live on God's holy hill is the one who speaks the truth from "the hidden affection or feeling within." God's people don't utter the truth. It flows from their hearts as a natural fruit.