No, the Temple does not keep a record of who completed Ordinances for deceased persons.
The article found at https://www.familysearch.org/help/helpcenter/article/can-i-find-out-who-completed-the-temple-ordinance-for-my-ancestors gives a more complete answer'
"If the ordinance work was done before 1970 and it was proxy work, it should be listed on the TIB (Temple Index Bureau) cards. The proxy or heir was listed on these cards. This index is available on microfilm at the Family History Library in Salt Lake City in the special collections area. Microfilms do not circulate to family history centers or affiliate libraries.
"If the temple ordinance work was done after 1970, the temple does not keep a record of who reserved the family names nor who completed the ordinance, only that the ordinance was completed. In Family Tree, you can see the date and temple where ordinances were completed. No other information is recorded regarding ordinances."
You may be able to find some clues by checking out information about who has contributed information to the record of the person.
Here is a link to an article about a brand-new feature that will help you find this information. Unfortunately, it only goes back 25 months, not 25 years, but it will be very helpful in the future.
Can I humbly suggest, that you contact, the Headquarters of the Church, in "Temple Square" in "Salt Lake City", Utah, USA, directly, by telephone; and, inquire, as to, whom, and/or, where, you would direct such a request.
I would suggest such could NOT be done through 'FamilySearch'.
There are two (x2) databases involved with regards "Temple" Work in "Family Tree" of 'FamilySearch'.
There is a separate database for the actual "Temple" Work, that is the purview of the "Temple" Department of the Church.
I hope this helps.