I think it's been dealt with elsewhere but I'll do this one for the sake of completeness.
False:
- any connection to a place of worship
- kanapaṭī
- a loan from Sanskrit.
Correct but irrelevant:
- [Tamil] Gan/kan - to know /knowledge/eye,
- and (Tamil) "pathi" (Skt. पति- pati-) does indeed "refer to father/master/lord/belongs to. refers to the God," but the Sanskrit (Dravidian) word has dental /t/ unlike the word in question, which has retroflex /ṭ/
Might be true but is only tangentially relevant:
-
In Hindi there are words like gaNda, kandala etc..for cheek.
- and not because of any perceived semblance between gaṇḍ and "kan-" but due to a certain semantic link 'a cheek, elephant's temple' —not "a place of elephant worship" — but this word has no place in the etymology of the discussed Hindi word
- ... but neither is used, only gāl is.
True:
- /kanpaṭī/ or <kanapaṭī> means “temple” in the sense “side of the head”, not “temple” in the sense “place of worship”.

- "Pati- (actually /-paṭī/) could refer to "flat attachments, around the cloth or some object, like the ribbons or frame".
- Tamil (and other Dravidian [languages]) for “eye” is kaṇ with retroflex /ṇ/; the Hindi word for “temple” has dental /n/.
It has a fairly transparent etymology.
While 'cheek' has no relevance to it, a noun of an analoguous construction to the 'anatomic temple' is
H گلپٿا गलपटा galpaṭā [gal = gāl, q.v. + S. पट+कः], s.m. Cheek-bone.
comparable to the contraction of
kān 'ear' to
kan combined with the final element -paṭ- with the masculine ending -ā.
The second member of the compound occurs independently in the form given below, out of whose meanings there are several bearing relevance to the topic.
H پٿي पट्टी
paṭṭi [S. पट्ट+इका], s.f. A piece or
strip of cloth; bandage, ligature, swath, plaster, cataplasm; splints,
band, fillet, ribbon,
tape, brace, tie;
head-band,
a narrow plate of metal (worn across the turban by sepoys and their native officers); a rafter, or the whole row or series of rafters that cover one
side of a house; side piece of the frame of a bedstead ( =
pāṭī);
parting of the hair in the middle; side-locks of hair over each temple; lath (of split bamboo, &c.); spokes of a wheel; a ledge; line, row; a rule to draw lines by;
a small plank, board, tablet, table (as in 'plane-table'); a small rectangular board on which children write ( =
pāṭī); a morsel of betel-leaf made up with betel-nut, lime, &c. ( =
bīṛī;
pān); a foil, &c. ( =
paṭā);
piece, part, portion; division of a village; division of land into portions or
strips; holding or tenure in coparcenary; a written order or patent; a title to a certain tenure of land; list, statement, invoice, document (of any kind); public subscription paper; cess, assessment; — a kind of sweetmeat ( =
pāṭī): —
paṭṭī bāṅdhnā (-
par), To apply a bandage, &c. (to a sore or wound); to bandage (the eyes), to blindfold: —
paṭṭī-par qābiẓ rahnā, To retain in severalty: —
paṭṭī paṛhānā, v.t. To teach the letters (to a child) from the
paṭṭī or board; (
fig.) to explain (anything to anyone), to give a lesson (to); to advise, counsel; to put (one) up to (some trick or roguery); to cheat, deceive, take in: —
paṭṭī pakaṛ-ke hilte rahnā, A phrase used to denote either excessive weakness or excessive laziness: —
paṭṭī toṛnā, v.n. To be bedridden: —
paṭṭī-dār, s.m. Holder or proprietor of a
paṭṭī or share in a coparcenary village or estate, a coparcener: —
paṭṭī-dārī, s.f. Coparcenary tenure; an estate held in severalty: —
paṭṭī-dārī nā-mukammal, s.f. Coparcenary tenure where part of the land is divided and part held in common; tenure of an estate in partial severalty: —
paṭṭī denā, v.t. =
paṭṭī paṛhānā, q.v.: —
paṭṭī-wār, adj. & adv. According to shares, holdings, assessment, &c.:
— paṭṭiyāṅ jamānā (-par), To paste the hair down (on the temples).
(Platts Urdu and Classical Hindi, and English dictionary)