The Collaborative International Dictionary of English v.0.48:

Heedless \Heed"less\, a.
   Without heed or care; inattentive; careless; thoughtless;
   unobservant.
   [1913 Webster]

         O, negligent and heedless discipline!    --Shak.
   [1913 Webster]

         The heedless lover does not know
         Whose eyes they are that wound him so.   --Waller.
   -- Heed"less*ly, adv. -- Heed"less*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

heedlessly
    adv 1: without care or concern; "carelessly raised the
           children's hopes without thinking of their possible
           disappointment" [syn: carelessly, heedlessly]

Moby Thesaurus II by Grady Ward, 1.0:

91 Moby Thesaurus words for "heedlessly":
   a corps perdu, airily, any old way, any which way, anyhow,
   apathetically, bunglingly, carelessly, casually, clumsily,
   cursorily, desperately, disinterestedly, dispassionately,
   disregardfully, forgetfully, furiously, haphazardly,
   happen what may, hastily, head over heels, headfirst, headforemost,
   headlong, heels over head, helter-skelter, hit and miss,
   hit or miss, holus-bolus, hotheadedly, hurriedly, hurry-scurry,
   impetuously, inadvertently, inattentively, inconsiderately,
   indeliberately, insouciantly, involuntarily, lackadaisically,
   like crazy, like mad, listlessly, madly, messily, mindlessly,
   negligently, nonchalantly, offhand, offhandedly, once over lightly,
   overeagerly, overenthusiastically, overzealously, perfunctorily,
   precipitantly, precipitately, precipitously, promiscuously,
   ramble-scramble, recklessly, regardlessly, slam-bang, slap-bang,
   slapdash, sloppily, tactlessly, thoughtlessly, unadvisedly,
   uncalculatedly, unconcernedly, uncooperatively, undesignedly,
   unguardedly, unheedfully, unheedingly, unhelpfully,
   unintentionally, uninterestedly, unmindfully, unpremeditatedly,
   unreasoningly, unsolicitously, unthinkingly, unthoughtfully,
   unvigilantly, unwarily, wantonly, wildly, without premeditation,
   without willing