Thanissaro's translations are... unique. The word being used, as others have pointed out, is "mano", the leader of an irregular group of nouns called the "manogana" - "the group with mano as its leader".
The PED has [a huge article on mano][1], worth reading in full if you're interested. I've copied the gist of it below, but as you should see, it is probably misleading to translate it as "heart". There is a word for that, "hadaya", which is sometimes used as a synonym of mano, viññāṇa, etc., but also refers to the physical heart organ.
It is fair to say he is within his right to use poetic license in this case; it is, after all, poetry, and the mind and the heart are much the same in Buddhism. As you can see below, though, manas generally refers more to the thinking side of things, than the emotive or the substantial entity of "the heart" or "the mind".
>Mano & Mana(s); (nt.) [Vedic manaḥ, see etym. under maññati]
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>II. Meaning: mind, thought
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>1. Mano represents the intellectual functioning of consciousness, while viñnāṇa represents the field of sense and sense -- reaction ("perception"), and citta the subjective aspect of consciousness (cp. Mrs. Rh. D. Buddhist Psychology p. 19) -- The rendering with "mind" covers most of the connotation; sometimes it may be translated "thought. As "mind" it embodies the rational faculty of man which, as the subjective side in our relation to the objective world, may be regarded as a special sense, acting on the world, a sense adapted to the rationality (reasonableness, dhamma) of the phenomena, as our eye is adapted to the visibility of the latter.
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>3. **As regards the relation of manas to citta, it may be stated that citta is more substantial (as indicated by translation "heart")**, more elemental as the seat of emotion, whereas manas is the finer element, a subtler feeling or thinking as such. See also citta2 I., and on rel. to viññāṇa & citta see citta;2 IV. 2b. In the more popular opinion and general phraseology however manas is almost synonymous with citta as opposed to body, cittaŋ iti pi mano iti pi S ii.94.
[1]: http://dsalsrv02.uchicago.edu/cgi-bin/philologic/getobject.pl?c.2:1:3860.pali