The Collaborative International Dictionary of English v.0.48:

Heartily \Heart"i*ly\ (h[aum]rt"[i^]*l[y^]), adv. [From
   Hearty.]
   1. From the heart; with all the heart; with sincerity.
      [1913 Webster]

            I heartily forgive them.              --Shak.
      [1913 Webster]

   2. With zeal; actively; vigorously; willingly; cordially; as,
      he heartily assisted the prince.
      [1913 Webster]

   To eat heartily, to eat freely and with relish. --Addison.

   Syn: Sincerely; cordially; zealously; vigorously; actively;
        warmly; eagerly; ardently; earnestly.
        [1913 Webster]

WordNet (r) 3.0 (2006):

heartily
    adv 1: with gusto and without reservation; "the boy threw
           himself heartily into his work"
    2: in a hearty manner; "`Yes,' the children chorused heartily";
       "We welcomed her warmly" [syn: heartily, cordially,
       warmly]

Moby Thesaurus II by Grady Ward, 1.0:

79 Moby Thesaurus words for "heartily":
   actively, agreeably, amiably, amicably, animatedly, ardently,
   arm in arm, breathlessly, briskly, con brio, congenially,
   cordially, deafeningly, devotedly, devoutly, earnestly,
   energetically, enthusiastically, excitedly, exuberantly,
   familiarly, favorably, fervently, fervidly, firmly, forcefully,
   forcibly, friendliwise, friendly, gaily, genially, glowingly,
   hand in hand, heart and soul, heatedly, impassionedly,
   imperviously, impregnably, intensely, intently, intimately,
   invincibly, invulnerably, irresistibly, keenly, kindly, loudly,
   lustily, mightily, passionately, perfervidly, pleasantly,
   powerfully, pungently, resistantly, robustly, ruggedly, seriously,
   sincerely, soundly, spiritedly, stalwartly, staunchly, stoutly,
   strenuously, strongly, sturdily, unyieldingly, vehemently,
   vigorously, vivaciously, warmly, with elan, with gusto,
   with open arms, with pep, with zest, zealously, zestfully