You can also try using a ANS or other flourophores which specifically binding to beta sheets of protein and detect partial or complete unfolding of protein upon heating using RT-PCR.....for more detail read following papers...

http://www.nature.com/nprot/journal/v2/n9/full/nprot.2007.321.html

http://pubs.rsc.org/en/content/articlehtml/2012/ra/c2ra22368f

Hi , the most cheap and very powerful technique to study protein conformation is circular dichroism. I recommend you to check this papers of Greenfield:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2728378/

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2752288/

On the other hand, 2D 1H-15N HSQC experiments could provide you more more information (at residue level) but this is more expensive because you need to label your protein...NMR would be a next step in your study.

Circular dichroism is the easier technique in order to observe changes in protein conformation with the temperature, but FTIR is also a powerful technique altough this last requires a more complicated analysis.

For solution state CD is the best while solid state FTIR is the best

CD would be the preferred technique to use. However, be aware that analysing the changes in α-helices or β-sheet might be difficult. To be able to calculate secondary structure with e.g Dichroweb you need to go down to wavelengths below 200nm. This require delicate handling of your sample as well as choice of buffers.

ANS (or other fluorophores) might be a good choice depending on your protein some proteins e.g BSA and fatty acid binding protein and thiopurine methyltransferase binds in the native state and you can easily monitor the release of ANS upon unfolding other proteins behaves differently e.g carbonic anhydrase that binds preferentially in the molten globule state. 

Nearly all "optical spectrocopies" (Raman,Infrared, FTinfrared, UV dichroism, vibrational dichroism etc) are useful for determining either the percentages contents of secondary structural  elements (hélices, strands, turns and coil) or the relative changes in structures from the shapes of the structural bands associated to secondary structutre

Thus, a lot of quantitative methods are usable (see our publications for Raman spectroscopy).