I'm not sure who the composers are for each of the temple films' soundtracks, but the soundtracks were almost certainly composed by contract specifically for the temple films. Because the temple film isn't distributed publicly, and because the Church hasn't made a point of distributing soundtracks even for films that
are distributed publicly, I don't expect the Church to provide the temple film soundtracks for download anytime soon.
It's much easier to find music composer information for commercially-distributed church films, and I wouldn't be surprised if some of the same composers helped out with the temple film soundtracks. Some of the better-known composers for church-related movie soundtracks are Merrill Jenson, Kurt Bestor, Sam Cardon, and Lex de Azevedo, though that's not a comprehensive list. I would recommend any of their music.
If you like the temple film soundtrack music, your best bet is to attend the temple more often.
