Given the standard Scotchflex type ribbon cable, 50 mil pitch, 28 ga, I'm wondering how much current it's OK to run through it. 3M and some others don't specify. Two sources suggest 1 amp. Harting specs 2.1.
It certainly matters what the cooling situation is, and what adjacent conductors are doing.
Looks like, in free still air, temp rise is under 10C for a single conductor at 3 amps, and under 10C at 1.5 amps if all its neighbors are running at the same current. Neither case feels hot.
My Flir imager doesn't resolve the temp of these tiny things very well.
Two parallel wires should be conservative at 3 amps per pair.