The Collaborative International Dictionary of English v.0.48:

Hotly \Hot"ly\, adv. [From Hot, a.]
   1. In a hot or fiery manner; ardently; vehemently; violently;
      hastily; as, a hotly pursued.
      [1913 Webster]

   2. In a lustful manner; lustfully. --Dryden.
      [1913 Webster]

WordNet (r) 3.0 (2006):

hotly
    adv 1: in a heated manner; "`To say I am behind the strike is so
           much nonsense,' declared Mr Harvey heatedly"; "the
           children were arguing hotly" [syn: heatedly, hotly]

Moby Thesaurus II by Grady Ward, 1.0:

28 Moby Thesaurus words for "hotly":
   ardently, demonically, desperately, doggedly, energetically,
   enthusiastically, fanatically, fervently, fervidly, feverishly,
   fiercely, frantically, frenetically, furiously, glowingly,
   heatedly, intensively, like mad, like one possessed, madly,
   passionately, persistently, severely, uncontrollably, violently,
   warmly, wildly, zealously