The Collaborative International Dictionary of English v.0.48:

Unthinking \Un*think"ing\, a.
   1. Not thinking; not heedful; thoughtless; inconsiderate; as,
      unthinking youth.
      [1913 Webster]

   2. Not indicating thought or reflection; thoughtless.
      [1913 Webster]

            With earnest eyes, and round unthinking face,
            He first the snuffbox opened, then the case. --Pope.
      [1913 Webster] -- Un*think"ing*ly, adv. --
      Un*think"ing*ness, n.
      [1913 Webster]

WordNet (r) 3.0 (2006):

unthinkingly
    adv 1: in a thoughtless manner; "he stared thoughtlessly at the
           picture" [syn: thoughtlessly, unthinkingly,
           unthinking] [ant: thoughtfully]