Article II, Section 2 of the U.S. Constitution provides that:
"The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session."
I don't see anything about the end of the current Congress, though you might be right. (If so, and you can establish that through a reference, it would be appreciated.)
For purposes of recess appointments, a session ends with the sine diem,which is currently targeted for December 16. So that would be the end of the current session, not the end of the "next" session. The scheduled recesses (as opposed to the sine diem recess) are intra-session.
However, Obama is the sitting president until the next president is sworn into office. Inauguration day 2017 is January 20. The first scheduled recess of the Senate is MLK Day, January 18. If Obama managed to make an intra-session recess appointment on that day, his appointee would serve until sine diem of the next session after that, which would be sometime in December 2018.