Can a person from outside New York get a temporary card to do a family research project

I believe you can but get more information online. You can always Google that information on a computer or smartphone.

Yes. From the website https://www.nypl.org/get-library-card#applicants%20outside%20state If you do not live, work, attend school or pay property tax in New York State and are visiting the library and seeking temporary cardholder privileges, apply online. Later, you can validate and pick up your card in person. Privileges will be granted for a period of 3 days or 3 months, depending on the length of your stay.