The Collaborative International Dictionary of English v.0.48:

Cordiality \Cor*dial"i*ty\ (k[^o]r*j[a^]l"[i^]*t[y^] or
   k[^o]r`d[i^]*[a^]l"-; 106), n.; pl. Cordialities (-t[i^]z).
   [LL. cordialitas, fr. cordialis sincere: cf. F.
   cordialit['e].]
   1. Relation to the heart. [Obs.]
      [1913 Webster]

            That the ancients had any respect of cordiality or
            reference unto the heart, will much be doubted.
                                                  --Sir T.
                                                  Browne.
      [1913 Webster]

   2. Sincere affection and kindness; warmth of regard;
      heartiness. --Motley.
      [1913 Webster]

WordNet (r) 3.0 (2006):

cordiality
    n 1: a cordial disposition [syn: amity, cordiality]

Moby Thesaurus II by Grady Ward, 1.0:

18 Moby Thesaurus words for "cordiality":
   agreeability, agreeableness, amiability, approbation, approval,
   enjoyableness, favor, geniality, gratefulness, mutuality,
   pleasance, pleasantness, reciprocity, responsiveness,
   sweetness and light, sympathy, understanding, warmth