This comes from 1964. (February 3, in fact, Museum of Broadcasting curator Wally Podrazik informs me.) In the first number we see, Shirley doesn't do any singing, but she's serenaded by The Gang, with one of my all-time favorite songs, "I'll Be Seeing You." (As it happens, the song was the title of a 1944 movie that Shirley Temple was in, though it wasn't written for the film, but came along six years earlier, written by Sammy Fain and Irving Kahal). She does sing along at the very end, though it's with the whole group, so we really don't hear anything from her.
But we do in the second number, which is a treat, as well, since it's Shirley not only singing "Make Someone Happy" (from the previously-discussed musical, Do Re Mi, by Comden & Green and Jule Styne), but she's joined by series regular Leslie Uggams -- and further, they both do a very nice bit of dancing.
And rounding out the fun is that for the third song we get to see a solo by Bob McGrath, just five years before he began starring in 1969 as 'Bob' in a new show on PBS called Sesame Street. (Alas, the song he sings is the least-interesting of the bunch. But still, it's a treat to see "early Bob.")
It was a good period for alumni of Sing Along with Mitch, because only two years earlier, in 1967, Leslie Uggams won a Tony Award as Best Actress in a Musical, for Hallelujah, Baby. (A show written -- oddly enough, again -- by...Comden & Green, and Jule Styne!)
NOTE: An earlier version of this piece had the date wrong, referring to it also as 1969.
But mainly -- and without question -- the real treat here is seeing the grown-up Shirley Temple.