The Collaborative International Dictionary of English v.0.48:

Warmly \Warm"ly\, adv.
   In a warm manner; ardently.
   [1913 Webster]

WordNet (r) 3.0 (2006):

warmly
    adv 1: in a hearty manner; "`Yes,' the children chorused
           heartily"; "We welcomed her warmly" [syn: heartily,
           cordially, warmly]
    2: in a warm manner; "warmly dressed"; "warm-clad skiers" [syn:
       warmly, warm]

Moby Thesaurus II by Grady Ward, 1.0:

63 Moby Thesaurus words for "warmly":
   agreeably, amiably, amicably, ardently, arm in arm, benignantly,
   benignly, breathlessly, congenially, cordially, effectively,
   eloquently, enthusiastically, excitedly, expressively, exuberantly,
   familiarly, favorably, fervently, fervidly, feverishly, fluently,
   forcefully, friendliwise, friendly, genially, glibly, glowingly,
   good, graphically, hand in hand, heart and soul, heartily,
   heatedly, hotly, humanely, humanly, impassionedly, impressively,
   in glowing terms, intensely, intimately, keenly, kindheartedly,
   kindly, meaningfully, nicely, passionately, pleasantly, powerfully,
   smoothly, softheartedly, spiritedly, strikingly, tellingly,
   tenderheartedly, vehemently, vigorously, vividly, warmheartedly,
   well, with open arms, zealously