Tafsir of Al-Humazah 104:7

This means that it ascends to the centers of the hearts and envelops them. The heart is specifically mentioned because it is the most delicate part of the body and the most intensely pained by the slightest harm that touches it. Alternatively, it is because the heart is the seat of deviant beliefs, malicious intentions, and vile dispositions, as well as the origin of evil deeds; thus, it is the most fitting [part of the body] for what preceded [the description of the Fire].

'Abd ibn Humayd and Ibn Abi Hatim narrated from Muhammad ibn Ka'b that he said regarding this verse: "It consumes everything of him until it reaches his heart. Once it reaches his heart, his creation begins anew [in a cycle of suffering]."

It is also permissible that the "mounting" refers to cognitive perception or [figurative] speech. Since every person being punished has a portion of the Fire according to the magnitude of their sins—which stem from the attributes of their hearts—it is said that it inspects the hearts, which are the repositories of sins, so that it knows what is within them and recompenses each individual according to the attributes they possess that necessitate torment.

The masters of [Sufi] allusion state that what has been mentioned is a reference to the spiritual torment, which is the most severe form of punishment.