fan letter(n = noun.communication) - a letter that is a piece of fan mail;
is a kind of letter, missive
is a part of fan mail

air letter, airmail letter, alluvial fan, attic fan, black letter, block letter, business letter, capital letter, chain letter, commercial letter of credit, cover letter, covering letter, crank letter, dead letter, electric fan, encyclical letter, exhaust fan, fan, fan belt, fan blade, fan dance, fan fern, fan mail, fan out, fan palm, fan shaped, fan tan, fan the flame, fan tracery, fan vaulting, form letter, investment letter, letter, letter a, letter b, letter bomb, letter bond, letter box, letter c, letter carrier, letter case, letter d, letter e, letter f, letter g, letter h, letter i, letter j, letter k, letter l, letter m, letter n, letter o, letter of credit, letter of intent, letter of jeremiah, letter of mark and reprisal, letter of marque, letter of the alphabet, letter opener, letter p, letter paper, letter q, letter r, letter s, letter security, letter stock, letter t, letter telegram, letter u, letter v, letter w, letter writer, letter x, letter y, letter z, love letter, lower-case letter, market letter, miniature fan palm, motion-picture fan, night letter, open letter, personal letter, polyphonic letter, runic letter, scarlet letter, sea fan, sea letter, short letter, small letter, sports fan, to the letter, traveler's letter of credit, traveller's letter of credit, upper-case letter, varsity letter