The question is a little unclear to me, but I think it predominantly concerns fixation on sin within the "domain" of the heart rather than the mind as understood within modern Western societies that speak English. It also asks why anatomical members involved directly in sin, such as reproductive organs in sexual sins, are not implicated instead of the heart.
Anatomical confusion and metaphorical language
The heart and mind in biblical texts rarely correspond literally to human anatomical organs. In fact, sometimes other anatomical members are actually translated in anatomically inaccurate ways to help modern English readers understand ancient metaphorical language and/or idioms.
For example, the Hebrew word כִּלְיָה (kilyah) occurs approximately 31 times in the Hebrew Bible and anatomically/literally refers to the "kidney" or "entrails." However, it also carries the idiomatic sense of "the innermost, most secret part of man" (and can also refer to "the interior of the wheat grain").
Since English metaphorically uses “heart” to represent one’s inner feelings and convictions, the figurative sense of כִּלְיָה (kilyah) is often rendered with “heart” or “mind” in English translation. This figurative use for the inner self occurs mainly in poetry....
As such, where it occurs in the Hebrew Bible, depending on context it might be translated
literally as the anatomical "kidney" (particularly when referring to part(s) of sacrificial animals; e.g., Exodus 29:13, 22; Leviticus 3:4, 10, 15);
metaphorically referring to the human conscience (e.g., "heart," "inward parts," "mind," "soul." Examples include Job 19:27; Psalm 7:9; 16:7; 26:2; 73:21; 139:13; Proverbs 23:16; Jeremiah 17:10; Lamentations 3:13); or
idiomatically as a kernel of wheat (Deuteronomy 32:14).
Conversely, Hebrew has words for "heart" (e.g., לֵב / lev)—as well as "mind"—which are also used metaphorically (and sometimes interchangeably with כִּלְיָה / kilyah).
The thinking heart and the feeling mind
The ancient world did not share our modern Western idea of a mind and heart dichotomy. As an illustrative example, Genesis 8:21 states that "the inclination of the human heart is evil from youth" (NRSV). The word translated as "heart" in the Hebrew Masoretic Text (MT) here is לֵב (lev), which often carries the sense of "mind" in contrast to כִּלְיָה (kilyah) when the latter is translated as "heart" (this verse is an example of the interchangeability of these terms as noted previously). The Septuagint, an early Greek translation of the Hebrew Bible (hereinafter abbreviated "LXX"), focused on the "inclination" and translated this word as διάνοια (dianoia). An English translation of the LXX of Genesis 8:21 reads: "the intention of humankind is focused on what is evil from youth."
Ancient Greek has a bit more complicated set of relationships and overlaps concerning the "mind" and "heart." For example:
διάνοια (dianoia) is "the faculty of thinking, comprehending, and reasoning, understanding, intelligence, mind as the organ of νοεῖν" (or νόημα / noema). It is often translated in the senses of "mind" (also "thought(s)," "heart," "spirit," "senses," "judgment"), "disposition" (also "disposed," "courage," "intent" or "intention," "understanding"), or "to prepare to think hard" / "gird up the loins of the mind" (see 1 Peter 1:13 for this latter usage).
λογισμοί (logismoi, plural of λογισμός) refers to thoughts or imaginings (and can also refer to an "argument" as a set of rational thoughts). Various Greek texts refer to the διάνοια (dianoia) as the seat of the λογισμοί (logismoi).
νοῦς (nous) is also translated as "mind" as in the "seat of the thoughts, feelings" or "way of thinking, frame of mind." It can also carry the sense of "intention, desire."
καρδία (kardia) is generally translated as "heart." It can carry the literal anatomical sense, but also is seen as the "seat of physical, spiritual and mental life, ... as the center and source of physical life, ... [and] as center and source of the whole inner life, [with] its thinking, feeling, and volition."
Since the biblical writers did not share our modern heart/mind dichotomy, they also had no problem describing "thinking" as an activity that occurs in the "heart" (although this will depend somewhat on the English translation(s) you consult).
"Then the LORD saw ... that every intent of the thoughts of his heart was only evil continually" (Genesis 6:5, NKJV).
"Preserve me from violent men, who plan evil things in their hearts" (Psalm 140:1b–2, NKJV).
"For out of the heart proceed evil thoughts..." (Matthew 15:19, NKJV).
"He has scattered the proud in the imagination [διάνοια] of their hearts" (Luke 1:51b, NKJV).
"But Mary kept all these things and pondered them in her heart" (Luke 2:19, NKJV).
"For the word of God ... is a discerner of the thoughts and intents of the heart" (Hebrews 4:12, NKJV).
It is also clear from these examples that biblical texts often indicate that the heart and mind are full of self-deception. The νοῦς (nous) further is spoken about in the New Testament as being corrupted in some sense, and therefore in need of renewal and transformation.
"... to those who are defiled and unbelieving nothing is pure; but even their mind [νοῦς (nous)] and conscience are defiled" (Titus 1:15, NKJV).
"And do not be conformed to this world, but be transformed by the renewing of your mind [νοῦς (nous)]" (Romans 12:2, NKJV).
"But we have the mind [νοῦς (nous)] of Christ" (1 Corinthians 2:16, NKJV).
"you should no longer walk as the rest of the Gentiles walk, in the futility of their mind [νοῦς (nous)], having their understanding [διάνοια (dianoia)] darkened, being alienated from the life of God, because of the ignorance that is in them, because of the blindness of their heart [καρδία (kardia)]" (Ephesians 4:17–18, NKJV).
- And Paul then instructed the Ephesians to "be renewed in the spirit of your mind [νοῦς (nous)]" (Ephesians 4:23, NKJV).
Is there any practical lesson here?
An explanation from an Eastern Christian perspective follows (which I believe best makes sense of the original context and biblical texts, and is also consistent with ideas expressed by native-Greek-speaking patristic writers from early Christian history):
Emotions and reason are not, in reality, two separate things, but two aspects of the same inner process. Our emotions are always caused by thoughts; whether you're feeling an emotion, it's because of something you're thinking (possibly something quite rational). And everyone knows how our reasoning can be influenced by our emotions. These aren't two equal-and-opposite functions, but a single integrated process....
[R]eason and emotion aren't ... the only equipment we have. We possess many other overlapping and cofunctioning abilities—thoughts, memories, fantasies, will—which bubble together in the cauldron of the heart. They are integrated aspects of the whole person....
If you think about it, the mind has two "gears," forward and reverse. Forward gear is when you are thinking something through, following a line of thought, reasoning in a logical way—the dianoia, above. In English today, when we speak of "the mind" we mean those active ways of thinking (usually setting them opposite to "the heart" or emotions).
But the mind also has a "reverse gear": it can receive information. This is our ability to understand, comprehend, discern, or perceive. In biblical Greek it is called the nous ... ([as is other times the case,] the word doesn't mean in Scripture what it does in Aristotle and Plato)....
Broadly speaking, [the nous] is our capacity to encounter life firsthand, our receptive awareness.... If God were to interact with us, it would be by means of the nous, not through our emotions or our reasoning ability.... Here's an example of how the word nous is used in Scripture. When Christ appeared to his disciples after his resurrection, he "opened their nous to understand the Scriptures" ([Luke] 24:45). Since English translations say that he opened their "mind," you might have thought that he made them intellectually sharper, better equipped to defend the Scriptures. No, he enabled the disciples to perceive something; he enabled them to see the prophecies of his life and work woven through the Old Testament like a silver thread. It had been there all along, but they had been unable to see it. When Christ opened their nous it was like a grimy window being opened, and they suddenly could see these prophecies everywhere.
The biblical authors did not distinguish between reason and emotion as distinct human faculties. The false dichotomy between the head and heart is a modern idea which is anachronistic to the biblical texts. Such faculties and any associated anatomical organs are generally used metaphorically and should not be seen as the literal physical originating locations of sin.