If it is temporary financing (you know the loan will be satisfied/replaced with a long term loan) then IMO it would be temporary financing regardless if the permanent financing is with another lender.
The FFIEC has HMDA FAQs; one regarding temporary vs. short term financing is below:
Temporary Financing. When is a loan “temporary financing” such that it is exempt from reporting?
Answer: The regulation lists as examples of temporary financing construction loans and bridge loans. See 203.4(d)(3). Construction and bridge loans are illustrative, not exclusive, examples of temporary financing. The examples indicate that financing is temporary if it is designed to be replaced by permanent financing of a much longer term. A loan is not temporary financing merely because its term is short. For example, a lender may make a loan with a 1-year term to enable an investor to purchase a home, renovate it, and re-sell it before the term expires. Such a loan must be reported as a home purchase loan. See 203.2(h).