I hate to sound rude, but is there any literature on this topic?. I have done TMs in the distant past to check for fidelity of pairing after anealing or to find a proper anealing temp for reassociation or hybridization. Some calculations of delta G are made for the bonds made during anealing of oligos with target sequences. There must be papers in that area.

I do not think you can directly correlate the energetic changes measured in melting curves with H-bond strengths. There are a lot of other energetic components involved in the breaking/forming of the double-stranded DNA, which should be even more important than the H-bond (which by the way is in competition with H-bond with solvent molecules!). Hydrophobic, stacking, entropic and ionic effects (polyelectrolyte) are in fact the main contributors to the energetics of the equilibrium.

Perhaps this could help: A. N. Lane, T. C. Jenkins, Q. Rev. Biophys. 2000, 33, 255–306.

I agree with Vazquez. Check out this JACS paper (and the SI) from 2011:

DOI: 10.1021/ja201397e

You'll find a number of useful references for the calculation of thermodynamic parameters based on Tm data. Good luck!

If the structures are known, it can be calculated theoretically. But relationship between H-bond and Tm is not yet known to me. But it may be helpful if you refer 1) Structures and Properties of Multi-stranded Nucleic Acids Authors: Lane A.N.; Jenkins T.C.Source: Current Organic Chemistry, Volume 5, Number 8, August 2001 , pp. 845-869(25)

and 2) http://www.sciencedirect.com/science/journal/00039861Archives of Biochemistry and Biophysics Volume 453, Issue 1, 1 September 2006, Pages 26–31 A thermodynamic signature for drug–DNA binding mode, Jonathan B. Chaires may be helful. Try the best