Here Oliver Cowdery initially wrote mine heart. He and Joseph Smith undoubtedly pronounced the initial h in heart, so the source for this error is probably the King James biblical style that permits mine heart and thine heart. Oliver caught his error virtually immediately here in 𝓟 and rewrote the i as a y (there is no change in ink flow for this part of the correction); somewhat later, perhaps after redipping his quill, he crossed out the ne and the dot for the initial i (the ink flow for these two crossouts is somewhat heavier).
The Book of Mormon text has two occurrences of the archaic mine heart (in 1 Nephi 11:1 and Alma 29:1) but 35 occurrences of my heart (compared with 38 occurrences of mine heart in the King James Bible and 84 of my heart ). Note, in particular, the use of my heart in the very next clause in Helaman 13:5: “he hath put it into my heart”.
Similarly, there is one occurrence of thine heart in the Book of Mormon (in 1 Nephi 21:21, an Isaiah quote) but four occurrences of thy heart. Compare this with 107 occurrences of thine heart in the King James Bible against 19 occurrences of thy heart.
There are several other cases where mine and my compete with each other when followed by a vowel-initial word (or an h-initial word for which the h was silent for many speakers of Early Modern English). See, for instance, the discussion under Jacob 5:47 regarding the competition between mine hand and my hand in the Book of Mormon text. For other nouns, see under possessive pronouns in volume 3. For each case of mine versus my (as well as thine versus thy), the critical text will follow the earliest extant reading, thus my heart twice here in Helaman 13:5.
Summary: Accept in Helaman 13:5 Oliver Cowdery’s correction in 𝓟 of mine heart to my heart as the original reading.