Just wondering if anyone is familiar with any research that touches on this. It seems to be a largely untapped topic, other than Wooh-yun Jung's (1994) work.
University of Minnesota Center for Advanced Research on Language Acquisition maintains a very complete bibliography on speech acts in a variety of languages. It's not clear from your question whether you are interested in English only; there is a lot of Japanese work listed as well.
Here is the page on Thanking acts. It includes:
Coulmas, F. (1981).
Eisenstein, M. & Bodman, J. (1995).
Eisenstein, M. & Bodman, J. W. (1986).
Ferrara, K. (1994).
Hinkel, E. (1994).
Ide, R. (1998).
Kim, Y. (1994).
Kimura, K. (1994).
Kumatoridani, T. (1999).
Miyake, K. (1994).
Moriyama, T. (1999).
Nakata, T. (1989).
Ogawa, H. (1995).
So it's certainly a good place to start.