Getting Married - Fiance Visa

Im trying to get information for a friend.

He has a fiance from India who has recently arrived on a fiance visa. They plan to get married at a temple, and will therfore they need to give notice to marry at a Register Office.

The question is, does she need to get a certificate of approval from the home office before she can give notice to marry to a Registrar?

Or, is it that as she is here on a fiance visa, she does not need to obtain a certificate of approval?

The latter.
COAs are only necessary for people who came to UK for some other purpose than marriage - eg a Working Holidaymaker who decides to marry half-way through their stay...