Here's the story:
Pre-war 14 story NYC apartment building
Apartment on 3rd floor

Shower has two knobs (hot & cold), two similar knobs below for the bath. Plumbing in the apartment is original (this apt, can't speak for the folks upstairs or downstairs).

Turn on shower (mostly hot, a bit of cold water) and it's fine for a minute or so then becomes COLD. Not cooling off, but COLD. Eventually it gets back to normal but sometimes repeats itself. Not sure if this happens only if the cold is on or if would happen with only the hot water on (that'd be too hot to shower in and it's not my apartment so I haven't had time to experiment).

The sink does not have this problem.

Is it possible that somebody upstairs redid their plumbing and some mixing valve is sending cold water down the hot water pipe?

Any other ideas?