Briefly, thermometric analysis is analytical method, developing something like a profile for a substance that is gradually heated or cooled. As I understand it, a sample may melt, decompose, oxidize, or react with other components. This changes the profile, which is useful to determine identity, or purity. To me however, its very much a "black box" -- I do what I'm told, and I get a heating profile, or I don't and I report that. Sorry, I can't find a better answer in Wikipedia, but someone on our forum may come up with a better resource for you. I don't think its often taught at the undergraduate level, but its a worthwhile thing to learn.