I know phrases like "in situ" which means in the current place/position, is there another phrase for the temporal equivalent which means "at the moment"?
In sitū literally means "in place" or "in the place"—it doesn't necessarily have anything to do with the current place, and in fact usually means the original or proper place for something. For example, if archaeologists photograph an artifact "in situ", it's happening at the place where the artifact was found, not the museum it gets taken to later.
So if you want a temporal equivalent, you can use a bare ablative like tempore. Sallust frequently uses the phrase eā tempestāte for "at that time", but that's a fairly archaic usage of tempestas; I would adjust it to the more classical eō tempore.