Usage of the word "interimly" [closed]
You're correct in saying that you should have used the word temporarily, for example
I'm giving you a pat on the back for temporarily filling someone's else shoes!
If you really want to use the word interim then re-phrase to something like
I'm giving you a pat on the back for filling someone's else shoes in the interim!
As far as I'm aware 'interimely' isn't a valid word in the English language. It (and also 'interimly' which would be the expected spelling if it would become official) does not appear in any dictionary 1, 2, which is a good sign that it is 'not a word' (especially since 'interim' is a more educated non-slang term). There's always a chance that it could slip into 'wordedness' (not a word (also, not a word)) but it is fairly unginly sounding so I expect not.
"Interimly" as an adverb is a very rare usage; it's not something you'd use in general conversation or even most professional writing.
All of the Google Books search results for "interimly" appear to be used within a legal context; where the lawyers are trying to be very precise about a specified interim period.
EFFECTIVE DATE NOTE At 54 FR 1150 Jan 12 1989 §614.4320 was amended interimly by removing the words "and approved by the Farm Credit Administration" in the first sentence, effective Jan 6 1989. At 54 FR 50736 Dec 11 1989 the rule was adopted as final, effective upon the expiration of 30 days after publication, during which either or both Houses of Congress are in session Notice of effective date will be published in the FEDERAL REGISTER.
Code of Federal Regulations: 1985-1999, Part 600 to End: Banking, US Government Printing Office, 1990
Someone in the US Government reworded a regulation, and since Congress didn't object within a specified period, it became permanent. Even here, this might not be the best choice of words. I might use "provisionally" instead.
Just a supplement to the previous answers.
I also checked the Oxford English Dictionary (OED) and interimly does not appear there (and neither does interimely).
None of the following dictionaries have it: Merriam-Webster, Lexico (formerly Oxford), American Heritage, Collins, vocabulary.com, Macmillan, Cambridge, Wiktionary, Webster's New World College Dictionary, Fifth Ed. (via yourdictionary.com), Infoplease, dictionary.com, Webster's 1913 Dictionary, and freedictionary.org
The following dictionaries list interim as an adverb, meaning in the meantime, meanwhile (as in, Interim, take courage, and make your calculations anew), with a note that it is rare or even archaic: the OED, Lexico, Collins, Wiktionary, Infoplease, and dictionary.com.
Interimly is also not present in Black's Law Dictionary, 8th ed.
All these negative results notwithstanding, I think that it is pretty hard to argue against the results of the searching of google books that user Spencer quotes. Based on these results, I would say that interimly is rare, but certainly attested in legal literature.
Idiomatic rephrasings
As others have said, you can use temporarily or in the interim (where the latter assumes that the context makes it clear what intervening time the word interim refers to). See the answer by user KillingTime. It is also possibel to use ad interim (OED: 'for an intervening or temporary period of time; in the meantime') and per interim (OED: 'for the meantime; during the intervening time. Now rare'), as tchrist mentioned. Sample usage (from OED):
There should be, at least ad interim, a special military status for the territories.
There is nothing better than confessing our own soul per interim.
Thus in your case, it would be
I'm giving you a pat on the back for filling someone's else shoes ad interim!