That's an interesting addition to the iron wire demo: a glass rod to exaggerate the 'dip'.
The glass rod makes sense because it's non-conductive enough to not be too dangerous, I would think.
The graphing on the video really makes the phase transitions remarkably visible, though.
I like it.
The video's description gives a little more detail as well as the reason for the slow, overall downward slope.
A steel wire is heated up by a current and it expands. When the phase transition temperature is reached the wire takes up additional energy which cools the wire down for a short time and shortens it.
This step can also be observed in the opposite direction when the current is switched off and the wire cools down. When the phase transition takes place the wire is heated up and it expands for a short time.
Over three cycles the thin wire gets already worn out. Is is deformed so that the diameter, the heating power and the temperature is not equal along the wire and the phase change occurs more distributed over time.